Kooperativer Bibliotheksverbund

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Format: 1 online resource (932 pages)

Edition: 1st ed.

Note: Front Cover -- SURVEY SAMPLING THEORY AND APPLICATIONS -- SURVEY SAMPLING THEORY AND APPLICATIONS -- Copyright -- Dedication -- CONTENTS -- PREFACE -- DESCRIPTIONS OF CHAPTERS -- ACKNOWLEDGMENTS -- 1 - Preliminaries and Basics of Probability Sampling -- 1.1 INTRODUCTION -- 1.2 DEFINITIONS AND TERMINOLOGIES -- 1.2.1 Population and Unit -- 1.2.2 Finite and Infinite Populations -- 1.2.3 Sampling Frame -- 1.2.4 Parameter and Parameter Space -- 1.2.5 Complete Enumeration and Sample Survey -- 1.2.6 Sampling and Nonsampling Errors -- 1.2.7 Sample -- 1.2.8 Probability and Purposive Sampling -- 1.3 SAMPLING DESIGN AND INCLUSION PROBABILITIES -- 1.3.1 Sampling Design -- 1.3.2 Inclusion Probabilities -- 1.3.3 Consistency Conditions of Inclusion Probabilities -- 1.3.4 Fixed Effective Size Design -- 1.3.5 Fixed Sample Size Design -- 1.4 METHODS OF SELECTION OF SAMPLE -- 1.4.1 Cumulative Total Method -- 1.4.2 Sampling Scheme -- 1.4.3 With and Without Replacement Sampling -- 1.4.4 Simple Random Sampling With Replacement -- 1.4.5 Simple Random Sampling Without Replacement -- 1.4.6 Probability Proportional to Size With Replacement Sampling -- 1.4.7 Probability Proportional to Size Without Replacement Sampling -- 1.4.8 Lahiri-Midzuno-Sen Sampling Scheme -- 1.5 HANURAV'S ALGORITHM -- 1.6 ORDERED AND UNORDERED SAMPLE -- 1.7 DATA -- 1.7.1 Sample Space -- 1.8 SAMPLING FROM HYPOTHETICAL POPULATIONS -- 1.8.1 Sampling From a Uniform Population -- 1.8.2 Sampling From a Normal Population -- 1.8.3 Sampling From a Binomial Population -- 1.9 EXERCISES -- 2 - Unified Sampling Theory: Design-Based Inference -- 2.1 INTRODUCTION -- 2.2 DEFINITIONS AND TERMINOLOGIES -- 2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs -- 2.2.2 Estimator and Estimate -- 2.2.3 Unbiased Estimator -- 2.2.4 Mean Square Error and Variance. , 2.2.5 Uniformly Minimum Variance Unbiased Estimator -- 2.3 LINEAR UNBIASED ESTIMATORS -- 2.3.1 Conditions of Unbiasedness -- 2.3.2 Horvitz-Thompson Estimator -- 2.3.3 Hansen-Hurwitz Estimator -- 2.3.4 Unbiased Ratio Estimator -- 2.3.5 Difference and Generalized Difference Estimator -- 2.4 PROPERTIES OF THE HORVITZ-THOMPSON ESTIMATOR -- 2.5 NONEXISTENCE THEOREMS -- 2.5.1 Unicluster Sampling Design -- 2.5.2 Class of Linear Homogeneous Unbiased Estimators -- 2.5.3 Optimality of the Horvitz-Thompson Estimator -- 2.5.4 Class of All Unbiased Estimators -- 2.5.5 Class of Linear Unbiased Estimators -- 2.6 ADMISSIBLE ESTIMATORS -- 2.7 SUFFICIENCY IN FINITE POPULATION -- 2.7.1 Sufficiency and Likelihood -- 2.7.2 Minimal Sufficient Statistic -- 2.7.3 Rao-Blackwellization -- 2.8 SAMPLING STRATEGIES -- 2.8.1 Unbiased Strategy -- 2.8.2 Uniformly Minimum Variance Unbiased Strategy -- 2.8.3 Admissible Strategies -- 2.8.4 Minimax Strategy -- 2.9 DISCUSSIONS -- 2.10 EXERCISES -- 3 - Simple Random Sampling -- 3.1 INTRODUCTION -- 3.2 SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT -- 3.2.1 Sampling Scheme -- 3.2.2 Estimation of Population Mean and Variance -- 3.2.3 Estimation of Population Covariance -- 3.2.4 Estimation of Population Proportion -- 3.2.5 Estimation of Domain Mean and Total -- 3.3 SIMPLE RANDOM SAMPLING WITH REPLACEMENT -- 3.3.1 Sampling Scheme -- 3.3.2 Estimation of the Population Mean and Variance -- 3.3.3 Estimation of Population Proportion -- 3.3.4 Rao-Blackwellization -- 3.4 INTERVAL ESTIMATION -- 3.4.1 Confidence Intervals for Mean and Proportion -- 3.4.1.1 Large Sample Size -- 3.4.1.2 Small Sample Size -- 3.5 DETERMINATION OF SAMPLE SIZE -- 3.5.1 Consideration of the Cost of a Survey -- 3.5.2 Consideration of the Efficiency of Estimators -- 3.5.2.1 Given Variance -- 3.5.2.2 Given Coefficient of Variation -- 3.5.2.3 Given Margin of Permissible Error. , 3.5.3 Use of Chebyshev Inequality -- 3.6 INVERSE SAMPLING -- 3.6.1 Simple Random Sampling Without Replacement -- 3.6.2 Simple Random Sampling With Replacement -- 3.7 EXERCISES -- 4 - Systematic Sampling -- 4.1 INTRODUCTION -- 4.2 LINEAR SYSTEMATIC SAMPLING -- 4.2.1 Linear Systematic Sampling With N/n=k an Integer -- 4.2.2 Linear Systematic Sampling With N/n=k Not an Integer -- 4.2.3 Estimation of the Population Mean and Its Variance -- 4.2.4 Nonexistence of Unbiased Variance Estimator -- 4.3 EFFICIENCY OF SYSTEMATIC SAMPLING -- 4.3.1 Comparison With Simple Random Sampling -- 4.3.2 Comparison With Stratified Sampling -- 4.3.3 Random Arrangement of Units -- 4.3.4 Population With Linear Trend -- 4.3.4.1 End Corrections -- 4.3.4.2 Balanced Systematic Sampling -- 4.3.5 Population With Periodic Variation -- 4.3.6 Autocorrelated Population -- 4.4 LINEAR SYSTEMATIC SAMPLING USING FRACTIONAL INTERVAL -- 4.5 CIRCULAR SYSTEMATIC SAMPLING -- 4.5.1 Circular Systematic Sampling With k=N/n as an Integer -- 4.5.2 Circular Systematic Sampling With N/n is Not an Integer -- 4.6 VARIANCE ESTIMATION -- 4.6.1 Single Systematic Sample -- 4.6.1.1 Random Arrangements of Units -- 4.6.1.2 Stratified Sampling With One Unit Per Stratum -- 4.6.1.3 Presence of Linear Trend -- 4.6.1.4 Presence of Autocorrelation Between Successive Units -- 4.6.1.5 Splitting of a Systematic Sample -- 4.6.2 Several Systematic Samples -- 4.7 TWO-DIMENSIONAL SYSTEMATIC SAMPLING -- 4.8 EXERCISES -- 5 - Unequal Probability Sampling -- 5.1 INTRODUCTION -- 5.2 PROBABILITY PROPORTIONAL TO SIZE WITH REPLACEMENT SAMPLING SCHEME -- 5.2.1 Cumulative Total Method -- 5.2.2 Lahiri's Method -- 5.2.3 Hansen-Hurwitz Estimator and its Variance -- 5.2.4 Rao-Blackwellization -- 5.3 PROBABILITY PROPORTIONAL TO SIZE WITHOUT REPLACEMENT SAMPLING SCHEME -- 5.3.1 Raj's Estimator and its Variance -- 5.3.2 Rao-Blackwellization. , 5.3.2.1 Murthy's Estimator -- 5.4 INCLUSION PROBABILITY PROPORTIONAL TO MEASURE OF SIZE SAMPLING SCHEME -- 5.4.1 Inclusion Probability Proportional to Measure of Size Sampling With n=2 -- 5.4.1.1 Brewer's Sampling Scheme -- 5.4.1.2 Durbin's Sampling Scheme -- 5.4.1.3 Hanurav's Sampling Scheme -- 5.4.2 Inclusion Probability Proportional to Measure of Size Sampling with n 2 -- 5.4.2.1 Lahiri-Midzuno-Sen Sampling Design -- 5.4.2.2 Probability Proportionate to Size Systematic Sampling Scheme -- 5.4.2.3 Sampford's Sampling Scheme -- 5.4.2.3.1 Comparison of Efficiency -- 5.4.2.4 Poisson (or Bernoulli) Sampling -- 5.4.2.5 Use of Combinatorics -- 5.4.2.6 The Nearest Proportional to Size Sampling -- 5.5 PROBABILITY PROPORTIONAL TO AGGREGATE SIZE WITHOUT REPLACEMENT -- 5.6 RAO-HARTLEY-COCHRAN SAMPLING SCHEME -- 5.7 COMPARISON OF UNEQUAL (VARYING) PROBABILITY SAMPLING DESIGNS -- 5.8 EXERCISES -- 6 - Inference Under Superpopulation Model -- 6.1 INTRODUCTION -- 6.2 DEFINITIONS -- 6.2.1 Sampling Strategy -- 6.2.2 Noninformative Sampling Design -- 6.2.3 Design-Unbiased (or p-Unbiased) Estimator -- 6.2.4 Model-Unbiased (or ξ-Unbiased) Estimator -- 6.2.5 Model Design-Unbiased (or pξ-Unbiased) Estimator -- 6.2.6 Design-Based Inference -- 6.2.7 Model-Based Inference -- 6.2.8 Model-Assisted Inference -- 6.2.9 Optimal Estimator -- 6.2.10 Optimal Strategy -- 6.3 MODEL-ASSISTED INFERENCE -- 6.3.1 Optimal Design-Unbiased Predictors -- 6.3.1.1 Product Measure Model -- 6.3.1.2 Equicorrelation Model -- 6.3.1.3 Transformation Model -- 6.3.2 Optimal Model Design-Unbiased Prediction -- 6.3.3 Exchangeable Model -- 6.3.4 Random Permutation Model -- 6.4 MODEL-BASED INFERENCE -- 6.4.1 Optimal Model-Unbiased Prediction -- 6.4.1.1 Product Measure Model -- 6.4.1.2 Transformation Model -- 6.4.1.3 Multiple Regression Model -- 6.5 ROBUSTNESS OF DESIGNS AND PREDICTORS. , 6.5.1 Robustness of Predictors -- 6.5.2 Balanced Sampling Design -- 6.5.3 Polynomial Regression Model -- 6.5.4 Balanced Sample of Order k -- 6.5.5 Optimality of Balanced Sampling -- 6.6 BAYESIAN INFERENCE -- 6.6.1 Bayes Estimator -- 6.7 COMPARISON OF STRATEGIES UNDER SUPERPOPULATION MODELS -- 6.7.1 Hansen-Hurwitz Strategy With Others -- 6.7.2 Horvitz-Thompson and Rao-Hartley-Cochran Strategy -- 6.7.3 Horvitz-Thompson and Lahiri-Midzuno-Sen Strategy -- 6.7.4 Rao-Hartley-Cochran and Lahiri-Midzuno-Sen Strategy -- 6.8 DISCUSSIONS -- 6.9 EXERCISES -- 7 - Stratified Sampling -- 7.1 INTRODUCTION -- 7.2 DEFINITION OF STRATIFIED SAMPLING -- 7.3 ADVANTAGES OF STRATIFIED SAMPLING -- 7.4 ESTIMATION PROCEDURE -- 7.4.1 Estimation of Population Mean -- 7.4.1.1 Arbitrary Fixed Sample Size Design -- 7.4.1.2 Simple Random Sampling Without Replacement -- 7.4.1.3 Probability Proportional to Size With Replacement Sampling -- 7.4.1.4 Simple Random Sampling With Replacement -- 7.4.2 Estimation of Population Proportion -- 7.4.2.1 Simple Random Sampling Without Replacement -- 7.4.2.2 Simple Random Sampling With Replacement -- 7.4.3 Interval Estimation -- 7.5 ALLOCATION OF SAMPLE SIZE -- 7.5.1 Optimum Allocation for Fixed Cost -- 7.5.2 Optimum Allocation for Fixed Variance -- 7.5.3 Simple Random Sampling Without Replacement -- 7.5.4 Simple Random Sampling With Replacement -- 7.5.5 Probability Proportional to Size With Replacement Sampling -- 7.5.6 Neyman Optimum Allocation -- 7.5.7 Proportional Allocation -- 7.6 COMPARISON BETWEEN STRATIFIED AND UNSTRATIFIED SAMPLING -- 7.6.1 Simple Random Sampling Without Replacement -- 7.6.2 Probability Proportional to Size With Replacement Sampling -- 7.6.3 Inclusion Probability Proportional to Size Sampling Scheme -- 7.7 CONSTRUCTION OF STRATA -- 7.7.1 Optimum Points of Stratification -- 7.7.1.1 Proportional Allocation. , 7.7.1.2 Optimum Allocation.

Additional Edition: ISBN 0-12-811848-2

Additional Edition: ISBN 0-12-811897-0

Language: English

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Format: 1 Online-Ressource (xxvii, 899 Seiten) : , Diagramme.

ISBN: 978-0-12-811897-9

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-0-12-811848-1

Language: English

Keywords: Stichprobe

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URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: 1 online resource (932 pages)

Edition: 1st ed.

Note: Front Cover -- SURVEY SAMPLING THEORY AND APPLICATIONS -- SURVEY SAMPLING THEORY AND APPLICATIONS -- Copyright -- Dedication -- CONTENTS -- PREFACE -- DESCRIPTIONS OF CHAPTERS -- ACKNOWLEDGMENTS -- 1 - Preliminaries and Basics of Probability Sampling -- 1.1 INTRODUCTION -- 1.2 DEFINITIONS AND TERMINOLOGIES -- 1.2.1 Population and Unit -- 1.2.2 Finite and Infinite Populations -- 1.2.3 Sampling Frame -- 1.2.4 Parameter and Parameter Space -- 1.2.5 Complete Enumeration and Sample Survey -- 1.2.6 Sampling and Nonsampling Errors -- 1.2.7 Sample -- 1.2.8 Probability and Purposive Sampling -- 1.3 SAMPLING DESIGN AND INCLUSION PROBABILITIES -- 1.3.1 Sampling Design -- 1.3.2 Inclusion Probabilities -- 1.3.3 Consistency Conditions of Inclusion Probabilities -- 1.3.4 Fixed Effective Size Design -- 1.3.5 Fixed Sample Size Design -- 1.4 METHODS OF SELECTION OF SAMPLE -- 1.4.1 Cumulative Total Method -- 1.4.2 Sampling Scheme -- 1.4.3 With and Without Replacement Sampling -- 1.4.4 Simple Random Sampling With Replacement -- 1.4.5 Simple Random Sampling Without Replacement -- 1.4.6 Probability Proportional to Size With Replacement Sampling -- 1.4.7 Probability Proportional to Size Without Replacement Sampling -- 1.4.8 Lahiri-Midzuno-Sen Sampling Scheme -- 1.5 HANURAV'S ALGORITHM -- 1.6 ORDERED AND UNORDERED SAMPLE -- 1.7 DATA -- 1.7.1 Sample Space -- 1.8 SAMPLING FROM HYPOTHETICAL POPULATIONS -- 1.8.1 Sampling From a Uniform Population -- 1.8.2 Sampling From a Normal Population -- 1.8.3 Sampling From a Binomial Population -- 1.9 EXERCISES -- 2 - Unified Sampling Theory: Design-Based Inference -- 2.1 INTRODUCTION -- 2.2 DEFINITIONS AND TERMINOLOGIES -- 2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs -- 2.2.2 Estimator and Estimate -- 2.2.3 Unbiased Estimator -- 2.2.4 Mean Square Error and Variance. , 2.2.5 Uniformly Minimum Variance Unbiased Estimator -- 2.3 LINEAR UNBIASED ESTIMATORS -- 2.3.1 Conditions of Unbiasedness -- 2.3.2 Horvitz-Thompson Estimator -- 2.3.3 Hansen-Hurwitz Estimator -- 2.3.4 Unbiased Ratio Estimator -- 2.3.5 Difference and Generalized Difference Estimator -- 2.4 PROPERTIES OF THE HORVITZ-THOMPSON ESTIMATOR -- 2.5 NONEXISTENCE THEOREMS -- 2.5.1 Unicluster Sampling Design -- 2.5.2 Class of Linear Homogeneous Unbiased Estimators -- 2.5.3 Optimality of the Horvitz-Thompson Estimator -- 2.5.4 Class of All Unbiased Estimators -- 2.5.5 Class of Linear Unbiased Estimators -- 2.6 ADMISSIBLE ESTIMATORS -- 2.7 SUFFICIENCY IN FINITE POPULATION -- 2.7.1 Sufficiency and Likelihood -- 2.7.2 Minimal Sufficient Statistic -- 2.7.3 Rao-Blackwellization -- 2.8 SAMPLING STRATEGIES -- 2.8.1 Unbiased Strategy -- 2.8.2 Uniformly Minimum Variance Unbiased Strategy -- 2.8.3 Admissible Strategies -- 2.8.4 Minimax Strategy -- 2.9 DISCUSSIONS -- 2.10 EXERCISES -- 3 - Simple Random Sampling -- 3.1 INTRODUCTION -- 3.2 SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT -- 3.2.1 Sampling Scheme -- 3.2.2 Estimation of Population Mean and Variance -- 3.2.3 Estimation of Population Covariance -- 3.2.4 Estimation of Population Proportion -- 3.2.5 Estimation of Domain Mean and Total -- 3.3 SIMPLE RANDOM SAMPLING WITH REPLACEMENT -- 3.3.1 Sampling Scheme -- 3.3.2 Estimation of the Population Mean and Variance -- 3.3.3 Estimation of Population Proportion -- 3.3.4 Rao-Blackwellization -- 3.4 INTERVAL ESTIMATION -- 3.4.1 Confidence Intervals for Mean and Proportion -- 3.4.1.1 Large Sample Size -- 3.4.1.2 Small Sample Size -- 3.5 DETERMINATION OF SAMPLE SIZE -- 3.5.1 Consideration of the Cost of a Survey -- 3.5.2 Consideration of the Efficiency of Estimators -- 3.5.2.1 Given Variance -- 3.5.2.2 Given Coefficient of Variation -- 3.5.2.3 Given Margin of Permissible Error. , 3.5.3 Use of Chebyshev Inequality -- 3.6 INVERSE SAMPLING -- 3.6.1 Simple Random Sampling Without Replacement -- 3.6.2 Simple Random Sampling With Replacement -- 3.7 EXERCISES -- 4 - Systematic Sampling -- 4.1 INTRODUCTION -- 4.2 LINEAR SYSTEMATIC SAMPLING -- 4.2.1 Linear Systematic Sampling With N/n=k an Integer -- 4.2.2 Linear Systematic Sampling With N/n=k Not an Integer -- 4.2.3 Estimation of the Population Mean and Its Variance -- 4.2.4 Nonexistence of Unbiased Variance Estimator -- 4.3 EFFICIENCY OF SYSTEMATIC SAMPLING -- 4.3.1 Comparison With Simple Random Sampling -- 4.3.2 Comparison With Stratified Sampling -- 4.3.3 Random Arrangement of Units -- 4.3.4 Population With Linear Trend -- 4.3.4.1 End Corrections -- 4.3.4.2 Balanced Systematic Sampling -- 4.3.5 Population With Periodic Variation -- 4.3.6 Autocorrelated Population -- 4.4 LINEAR SYSTEMATIC SAMPLING USING FRACTIONAL INTERVAL -- 4.5 CIRCULAR SYSTEMATIC SAMPLING -- 4.5.1 Circular Systematic Sampling With k=N/n as an Integer -- 4.5.2 Circular Systematic Sampling With N/n is Not an Integer -- 4.6 VARIANCE ESTIMATION -- 4.6.1 Single Systematic Sample -- 4.6.1.1 Random Arrangements of Units -- 4.6.1.2 Stratified Sampling With One Unit Per Stratum -- 4.6.1.3 Presence of Linear Trend -- 4.6.1.4 Presence of Autocorrelation Between Successive Units -- 4.6.1.5 Splitting of a Systematic Sample -- 4.6.2 Several Systematic Samples -- 4.7 TWO-DIMENSIONAL SYSTEMATIC SAMPLING -- 4.8 EXERCISES -- 5 - Unequal Probability Sampling -- 5.1 INTRODUCTION -- 5.2 PROBABILITY PROPORTIONAL TO SIZE WITH REPLACEMENT SAMPLING SCHEME -- 5.2.1 Cumulative Total Method -- 5.2.2 Lahiri's Method -- 5.2.3 Hansen-Hurwitz Estimator and its Variance -- 5.2.4 Rao-Blackwellization -- 5.3 PROBABILITY PROPORTIONAL TO SIZE WITHOUT REPLACEMENT SAMPLING SCHEME -- 5.3.1 Raj's Estimator and its Variance -- 5.3.2 Rao-Blackwellization. , 5.3.2.1 Murthy's Estimator -- 5.4 INCLUSION PROBABILITY PROPORTIONAL TO MEASURE OF SIZE SAMPLING SCHEME -- 5.4.1 Inclusion Probability Proportional to Measure of Size Sampling With n=2 -- 5.4.1.1 Brewer's Sampling Scheme -- 5.4.1.2 Durbin's Sampling Scheme -- 5.4.1.3 Hanurav's Sampling Scheme -- 5.4.2 Inclusion Probability Proportional to Measure of Size Sampling with n 2 -- 5.4.2.1 Lahiri-Midzuno-Sen Sampling Design -- 5.4.2.2 Probability Proportionate to Size Systematic Sampling Scheme -- 5.4.2.3 Sampford's Sampling Scheme -- 5.4.2.3.1 Comparison of Efficiency -- 5.4.2.4 Poisson (or Bernoulli) Sampling -- 5.4.2.5 Use of Combinatorics -- 5.4.2.6 The Nearest Proportional to Size Sampling -- 5.5 PROBABILITY PROPORTIONAL TO AGGREGATE SIZE WITHOUT REPLACEMENT -- 5.6 RAO-HARTLEY-COCHRAN SAMPLING SCHEME -- 5.7 COMPARISON OF UNEQUAL (VARYING) PROBABILITY SAMPLING DESIGNS -- 5.8 EXERCISES -- 6 - Inference Under Superpopulation Model -- 6.1 INTRODUCTION -- 6.2 DEFINITIONS -- 6.2.1 Sampling Strategy -- 6.2.2 Noninformative Sampling Design -- 6.2.3 Design-Unbiased (or p-Unbiased) Estimator -- 6.2.4 Model-Unbiased (or ξ-Unbiased) Estimator -- 6.2.5 Model Design-Unbiased (or pξ-Unbiased) Estimator -- 6.2.6 Design-Based Inference -- 6.2.7 Model-Based Inference -- 6.2.8 Model-Assisted Inference -- 6.2.9 Optimal Estimator -- 6.2.10 Optimal Strategy -- 6.3 MODEL-ASSISTED INFERENCE -- 6.3.1 Optimal Design-Unbiased Predictors -- 6.3.1.1 Product Measure Model -- 6.3.1.2 Equicorrelation Model -- 6.3.1.3 Transformation Model -- 6.3.2 Optimal Model Design-Unbiased Prediction -- 6.3.3 Exchangeable Model -- 6.3.4 Random Permutation Model -- 6.4 MODEL-BASED INFERENCE -- 6.4.1 Optimal Model-Unbiased Prediction -- 6.4.1.1 Product Measure Model -- 6.4.1.2 Transformation Model -- 6.4.1.3 Multiple Regression Model -- 6.5 ROBUSTNESS OF DESIGNS AND PREDICTORS. , 6.5.1 Robustness of Predictors -- 6.5.2 Balanced Sampling Design -- 6.5.3 Polynomial Regression Model -- 6.5.4 Balanced Sample of Order k -- 6.5.5 Optimality of Balanced Sampling -- 6.6 BAYESIAN INFERENCE -- 6.6.1 Bayes Estimator -- 6.7 COMPARISON OF STRATEGIES UNDER SUPERPOPULATION MODELS -- 6.7.1 Hansen-Hurwitz Strategy With Others -- 6.7.2 Horvitz-Thompson and Rao-Hartley-Cochran Strategy -- 6.7.3 Horvitz-Thompson and Lahiri-Midzuno-Sen Strategy -- 6.7.4 Rao-Hartley-Cochran and Lahiri-Midzuno-Sen Strategy -- 6.8 DISCUSSIONS -- 6.9 EXERCISES -- 7 - Stratified Sampling -- 7.1 INTRODUCTION -- 7.2 DEFINITION OF STRATIFIED SAMPLING -- 7.3 ADVANTAGES OF STRATIFIED SAMPLING -- 7.4 ESTIMATION PROCEDURE -- 7.4.1 Estimation of Population Mean -- 7.4.1.1 Arbitrary Fixed Sample Size Design -- 7.4.1.2 Simple Random Sampling Without Replacement -- 7.4.1.3 Probability Proportional to Size With Replacement Sampling -- 7.4.1.4 Simple Random Sampling With Replacement -- 7.4.2 Estimation of Population Proportion -- 7.4.2.1 Simple Random Sampling Without Replacement -- 7.4.2.2 Simple Random Sampling With Replacement -- 7.4.3 Interval Estimation -- 7.5 ALLOCATION OF SAMPLE SIZE -- 7.5.1 Optimum Allocation for Fixed Cost -- 7.5.2 Optimum Allocation for Fixed Variance -- 7.5.3 Simple Random Sampling Without Replacement -- 7.5.4 Simple Random Sampling With Replacement -- 7.5.5 Probability Proportional to Size With Replacement Sampling -- 7.5.6 Neyman Optimum Allocation -- 7.5.7 Proportional Allocation -- 7.6 COMPARISON BETWEEN STRATIFIED AND UNSTRATIFIED SAMPLING -- 7.6.1 Simple Random Sampling Without Replacement -- 7.6.2 Probability Proportional to Size With Replacement Sampling -- 7.6.3 Inclusion Probability Proportional to Size Sampling Scheme -- 7.7 CONSTRUCTION OF STRATA -- 7.7.1 Optimum Points of Stratification -- 7.7.1.1 Proportional Allocation. , 7.7.1.2 Optimum Allocation.

Additional Edition: ISBN 0-12-811848-2

Additional Edition: ISBN 0-12-811897-0

Language: English

UID:

Format: 1 online resource (932 pages)

Edition: 1st ed.

Note: Front Cover -- SURVEY SAMPLING THEORY AND APPLICATIONS -- SURVEY SAMPLING THEORY AND APPLICATIONS -- Copyright -- Dedication -- CONTENTS -- PREFACE -- DESCRIPTIONS OF CHAPTERS -- ACKNOWLEDGMENTS -- 1 - Preliminaries and Basics of Probability Sampling -- 1.1 INTRODUCTION -- 1.2 DEFINITIONS AND TERMINOLOGIES -- 1.2.1 Population and Unit -- 1.2.2 Finite and Infinite Populations -- 1.2.3 Sampling Frame -- 1.2.4 Parameter and Parameter Space -- 1.2.5 Complete Enumeration and Sample Survey -- 1.2.6 Sampling and Nonsampling Errors -- 1.2.7 Sample -- 1.2.8 Probability and Purposive Sampling -- 1.3 SAMPLING DESIGN AND INCLUSION PROBABILITIES -- 1.3.1 Sampling Design -- 1.3.2 Inclusion Probabilities -- 1.3.3 Consistency Conditions of Inclusion Probabilities -- 1.3.4 Fixed Effective Size Design -- 1.3.5 Fixed Sample Size Design -- 1.4 METHODS OF SELECTION OF SAMPLE -- 1.4.1 Cumulative Total Method -- 1.4.2 Sampling Scheme -- 1.4.3 With and Without Replacement Sampling -- 1.4.4 Simple Random Sampling With Replacement -- 1.4.5 Simple Random Sampling Without Replacement -- 1.4.6 Probability Proportional to Size With Replacement Sampling -- 1.4.7 Probability Proportional to Size Without Replacement Sampling -- 1.4.8 Lahiri-Midzuno-Sen Sampling Scheme -- 1.5 HANURAV'S ALGORITHM -- 1.6 ORDERED AND UNORDERED SAMPLE -- 1.7 DATA -- 1.7.1 Sample Space -- 1.8 SAMPLING FROM HYPOTHETICAL POPULATIONS -- 1.8.1 Sampling From a Uniform Population -- 1.8.2 Sampling From a Normal Population -- 1.8.3 Sampling From a Binomial Population -- 1.9 EXERCISES -- 2 - Unified Sampling Theory: Design-Based Inference -- 2.1 INTRODUCTION -- 2.2 DEFINITIONS AND TERMINOLOGIES -- 2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs -- 2.2.2 Estimator and Estimate -- 2.2.3 Unbiased Estimator -- 2.2.4 Mean Square Error and Variance. , 2.2.5 Uniformly Minimum Variance Unbiased Estimator -- 2.3 LINEAR UNBIASED ESTIMATORS -- 2.3.1 Conditions of Unbiasedness -- 2.3.2 Horvitz-Thompson Estimator -- 2.3.3 Hansen-Hurwitz Estimator -- 2.3.4 Unbiased Ratio Estimator -- 2.3.5 Difference and Generalized Difference Estimator -- 2.4 PROPERTIES OF THE HORVITZ-THOMPSON ESTIMATOR -- 2.5 NONEXISTENCE THEOREMS -- 2.5.1 Unicluster Sampling Design -- 2.5.2 Class of Linear Homogeneous Unbiased Estimators -- 2.5.3 Optimality of the Horvitz-Thompson Estimator -- 2.5.4 Class of All Unbiased Estimators -- 2.5.5 Class of Linear Unbiased Estimators -- 2.6 ADMISSIBLE ESTIMATORS -- 2.7 SUFFICIENCY IN FINITE POPULATION -- 2.7.1 Sufficiency and Likelihood -- 2.7.2 Minimal Sufficient Statistic -- 2.7.3 Rao-Blackwellization -- 2.8 SAMPLING STRATEGIES -- 2.8.1 Unbiased Strategy -- 2.8.2 Uniformly Minimum Variance Unbiased Strategy -- 2.8.3 Admissible Strategies -- 2.8.4 Minimax Strategy -- 2.9 DISCUSSIONS -- 2.10 EXERCISES -- 3 - Simple Random Sampling -- 3.1 INTRODUCTION -- 3.2 SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT -- 3.2.1 Sampling Scheme -- 3.2.2 Estimation of Population Mean and Variance -- 3.2.3 Estimation of Population Covariance -- 3.2.4 Estimation of Population Proportion -- 3.2.5 Estimation of Domain Mean and Total -- 3.3 SIMPLE RANDOM SAMPLING WITH REPLACEMENT -- 3.3.1 Sampling Scheme -- 3.3.2 Estimation of the Population Mean and Variance -- 3.3.3 Estimation of Population Proportion -- 3.3.4 Rao-Blackwellization -- 3.4 INTERVAL ESTIMATION -- 3.4.1 Confidence Intervals for Mean and Proportion -- 3.4.1.1 Large Sample Size -- 3.4.1.2 Small Sample Size -- 3.5 DETERMINATION OF SAMPLE SIZE -- 3.5.1 Consideration of the Cost of a Survey -- 3.5.2 Consideration of the Efficiency of Estimators -- 3.5.2.1 Given Variance -- 3.5.2.2 Given Coefficient of Variation -- 3.5.2.3 Given Margin of Permissible Error. , 3.5.3 Use of Chebyshev Inequality -- 3.6 INVERSE SAMPLING -- 3.6.1 Simple Random Sampling Without Replacement -- 3.6.2 Simple Random Sampling With Replacement -- 3.7 EXERCISES -- 4 - Systematic Sampling -- 4.1 INTRODUCTION -- 4.2 LINEAR SYSTEMATIC SAMPLING -- 4.2.1 Linear Systematic Sampling With N/n=k an Integer -- 4.2.2 Linear Systematic Sampling With N/n=k Not an Integer -- 4.2.3 Estimation of the Population Mean and Its Variance -- 4.2.4 Nonexistence of Unbiased Variance Estimator -- 4.3 EFFICIENCY OF SYSTEMATIC SAMPLING -- 4.3.1 Comparison With Simple Random Sampling -- 4.3.2 Comparison With Stratified Sampling -- 4.3.3 Random Arrangement of Units -- 4.3.4 Population With Linear Trend -- 4.3.4.1 End Corrections -- 4.3.4.2 Balanced Systematic Sampling -- 4.3.5 Population With Periodic Variation -- 4.3.6 Autocorrelated Population -- 4.4 LINEAR SYSTEMATIC SAMPLING USING FRACTIONAL INTERVAL -- 4.5 CIRCULAR SYSTEMATIC SAMPLING -- 4.5.1 Circular Systematic Sampling With k=N/n as an Integer -- 4.5.2 Circular Systematic Sampling With N/n is Not an Integer -- 4.6 VARIANCE ESTIMATION -- 4.6.1 Single Systematic Sample -- 4.6.1.1 Random Arrangements of Units -- 4.6.1.2 Stratified Sampling With One Unit Per Stratum -- 4.6.1.3 Presence of Linear Trend -- 4.6.1.4 Presence of Autocorrelation Between Successive Units -- 4.6.1.5 Splitting of a Systematic Sample -- 4.6.2 Several Systematic Samples -- 4.7 TWO-DIMENSIONAL SYSTEMATIC SAMPLING -- 4.8 EXERCISES -- 5 - Unequal Probability Sampling -- 5.1 INTRODUCTION -- 5.2 PROBABILITY PROPORTIONAL TO SIZE WITH REPLACEMENT SAMPLING SCHEME -- 5.2.1 Cumulative Total Method -- 5.2.2 Lahiri's Method -- 5.2.3 Hansen-Hurwitz Estimator and its Variance -- 5.2.4 Rao-Blackwellization -- 5.3 PROBABILITY PROPORTIONAL TO SIZE WITHOUT REPLACEMENT SAMPLING SCHEME -- 5.3.1 Raj's Estimator and its Variance -- 5.3.2 Rao-Blackwellization. , 5.3.2.1 Murthy's Estimator -- 5.4 INCLUSION PROBABILITY PROPORTIONAL TO MEASURE OF SIZE SAMPLING SCHEME -- 5.4.1 Inclusion Probability Proportional to Measure of Size Sampling With n=2 -- 5.4.1.1 Brewer's Sampling Scheme -- 5.4.1.2 Durbin's Sampling Scheme -- 5.4.1.3 Hanurav's Sampling Scheme -- 5.4.2 Inclusion Probability Proportional to Measure of Size Sampling with n 2 -- 5.4.2.1 Lahiri-Midzuno-Sen Sampling Design -- 5.4.2.2 Probability Proportionate to Size Systematic Sampling Scheme -- 5.4.2.3 Sampford's Sampling Scheme -- 5.4.2.3.1 Comparison of Efficiency -- 5.4.2.4 Poisson (or Bernoulli) Sampling -- 5.4.2.5 Use of Combinatorics -- 5.4.2.6 The Nearest Proportional to Size Sampling -- 5.5 PROBABILITY PROPORTIONAL TO AGGREGATE SIZE WITHOUT REPLACEMENT -- 5.6 RAO-HARTLEY-COCHRAN SAMPLING SCHEME -- 5.7 COMPARISON OF UNEQUAL (VARYING) PROBABILITY SAMPLING DESIGNS -- 5.8 EXERCISES -- 6 - Inference Under Superpopulation Model -- 6.1 INTRODUCTION -- 6.2 DEFINITIONS -- 6.2.1 Sampling Strategy -- 6.2.2 Noninformative Sampling Design -- 6.2.3 Design-Unbiased (or p-Unbiased) Estimator -- 6.2.4 Model-Unbiased (or ξ-Unbiased) Estimator -- 6.2.5 Model Design-Unbiased (or pξ-Unbiased) Estimator -- 6.2.6 Design-Based Inference -- 6.2.7 Model-Based Inference -- 6.2.8 Model-Assisted Inference -- 6.2.9 Optimal Estimator -- 6.2.10 Optimal Strategy -- 6.3 MODEL-ASSISTED INFERENCE -- 6.3.1 Optimal Design-Unbiased Predictors -- 6.3.1.1 Product Measure Model -- 6.3.1.2 Equicorrelation Model -- 6.3.1.3 Transformation Model -- 6.3.2 Optimal Model Design-Unbiased Prediction -- 6.3.3 Exchangeable Model -- 6.3.4 Random Permutation Model -- 6.4 MODEL-BASED INFERENCE -- 6.4.1 Optimal Model-Unbiased Prediction -- 6.4.1.1 Product Measure Model -- 6.4.1.2 Transformation Model -- 6.4.1.3 Multiple Regression Model -- 6.5 ROBUSTNESS OF DESIGNS AND PREDICTORS. , 6.5.1 Robustness of Predictors -- 6.5.2 Balanced Sampling Design -- 6.5.3 Polynomial Regression Model -- 6.5.4 Balanced Sample of Order k -- 6.5.5 Optimality of Balanced Sampling -- 6.6 BAYESIAN INFERENCE -- 6.6.1 Bayes Estimator -- 6.7 COMPARISON OF STRATEGIES UNDER SUPERPOPULATION MODELS -- 6.7.1 Hansen-Hurwitz Strategy With Others -- 6.7.2 Horvitz-Thompson and Rao-Hartley-Cochran Strategy -- 6.7.3 Horvitz-Thompson and Lahiri-Midzuno-Sen Strategy -- 6.7.4 Rao-Hartley-Cochran and Lahiri-Midzuno-Sen Strategy -- 6.8 DISCUSSIONS -- 6.9 EXERCISES -- 7 - Stratified Sampling -- 7.1 INTRODUCTION -- 7.2 DEFINITION OF STRATIFIED SAMPLING -- 7.3 ADVANTAGES OF STRATIFIED SAMPLING -- 7.4 ESTIMATION PROCEDURE -- 7.4.1 Estimation of Population Mean -- 7.4.1.1 Arbitrary Fixed Sample Size Design -- 7.4.1.2 Simple Random Sampling Without Replacement -- 7.4.1.3 Probability Proportional to Size With Replacement Sampling -- 7.4.1.4 Simple Random Sampling With Replacement -- 7.4.2 Estimation of Population Proportion -- 7.4.2.1 Simple Random Sampling Without Replacement -- 7.4.2.2 Simple Random Sampling With Replacement -- 7.4.3 Interval Estimation -- 7.5 ALLOCATION OF SAMPLE SIZE -- 7.5.1 Optimum Allocation for Fixed Cost -- 7.5.2 Optimum Allocation for Fixed Variance -- 7.5.3 Simple Random Sampling Without Replacement -- 7.5.4 Simple Random Sampling With Replacement -- 7.5.5 Probability Proportional to Size With Replacement Sampling -- 7.5.6 Neyman Optimum Allocation -- 7.5.7 Proportional Allocation -- 7.6 COMPARISON BETWEEN STRATIFIED AND UNSTRATIFIED SAMPLING -- 7.6.1 Simple Random Sampling Without Replacement -- 7.6.2 Probability Proportional to Size With Replacement Sampling -- 7.6.3 Inclusion Probability Proportional to Size Sampling Scheme -- 7.7 CONSTRUCTION OF STRATA -- 7.7.1 Optimum Points of Stratification -- 7.7.1.1 Proportional Allocation. , 7.7.1.2 Optimum Allocation.

Additional Edition: ISBN 0-12-811848-2

Additional Edition: ISBN 0-12-811897-0

Language: English

UID:

Format: 1 online resource (932 pages)

Edition: 1st ed.

Note: Front Cover -- SURVEY SAMPLING THEORY AND APPLICATIONS -- SURVEY SAMPLING THEORY AND APPLICATIONS -- Copyright -- Dedication -- CONTENTS -- PREFACE -- DESCRIPTIONS OF CHAPTERS -- ACKNOWLEDGMENTS -- 1 - Preliminaries and Basics of Probability Sampling -- 1.1 INTRODUCTION -- 1.2 DEFINITIONS AND TERMINOLOGIES -- 1.2.1 Population and Unit -- 1.2.2 Finite and Infinite Populations -- 1.2.3 Sampling Frame -- 1.2.4 Parameter and Parameter Space -- 1.2.5 Complete Enumeration and Sample Survey -- 1.2.6 Sampling and Nonsampling Errors -- 1.2.7 Sample -- 1.2.8 Probability and Purposive Sampling -- 1.3 SAMPLING DESIGN AND INCLUSION PROBABILITIES -- 1.3.1 Sampling Design -- 1.3.2 Inclusion Probabilities -- 1.3.3 Consistency Conditions of Inclusion Probabilities -- 1.3.4 Fixed Effective Size Design -- 1.3.5 Fixed Sample Size Design -- 1.4 METHODS OF SELECTION OF SAMPLE -- 1.4.1 Cumulative Total Method -- 1.4.2 Sampling Scheme -- 1.4.3 With and Without Replacement Sampling -- 1.4.4 Simple Random Sampling With Replacement -- 1.4.5 Simple Random Sampling Without Replacement -- 1.4.6 Probability Proportional to Size With Replacement Sampling -- 1.4.7 Probability Proportional to Size Without Replacement Sampling -- 1.4.8 Lahiri-Midzuno-Sen Sampling Scheme -- 1.5 HANURAV'S ALGORITHM -- 1.6 ORDERED AND UNORDERED SAMPLE -- 1.7 DATA -- 1.7.1 Sample Space -- 1.8 SAMPLING FROM HYPOTHETICAL POPULATIONS -- 1.8.1 Sampling From a Uniform Population -- 1.8.2 Sampling From a Normal Population -- 1.8.3 Sampling From a Binomial Population -- 1.9 EXERCISES -- 2 - Unified Sampling Theory: Design-Based Inference -- 2.1 INTRODUCTION -- 2.2 DEFINITIONS AND TERMINOLOGIES -- 2.2.1 Noninformative and Adaptive (Sequential) Sampling Designs -- 2.2.2 Estimator and Estimate -- 2.2.3 Unbiased Estimator -- 2.2.4 Mean Square Error and Variance. , 2.2.5 Uniformly Minimum Variance Unbiased Estimator -- 2.3 LINEAR UNBIASED ESTIMATORS -- 2.3.1 Conditions of Unbiasedness -- 2.3.2 Horvitz-Thompson Estimator -- 2.3.3 Hansen-Hurwitz Estimator -- 2.3.4 Unbiased Ratio Estimator -- 2.3.5 Difference and Generalized Difference Estimator -- 2.4 PROPERTIES OF THE HORVITZ-THOMPSON ESTIMATOR -- 2.5 NONEXISTENCE THEOREMS -- 2.5.1 Unicluster Sampling Design -- 2.5.2 Class of Linear Homogeneous Unbiased Estimators -- 2.5.3 Optimality of the Horvitz-Thompson Estimator -- 2.5.4 Class of All Unbiased Estimators -- 2.5.5 Class of Linear Unbiased Estimators -- 2.6 ADMISSIBLE ESTIMATORS -- 2.7 SUFFICIENCY IN FINITE POPULATION -- 2.7.1 Sufficiency and Likelihood -- 2.7.2 Minimal Sufficient Statistic -- 2.7.3 Rao-Blackwellization -- 2.8 SAMPLING STRATEGIES -- 2.8.1 Unbiased Strategy -- 2.8.2 Uniformly Minimum Variance Unbiased Strategy -- 2.8.3 Admissible Strategies -- 2.8.4 Minimax Strategy -- 2.9 DISCUSSIONS -- 2.10 EXERCISES -- 3 - Simple Random Sampling -- 3.1 INTRODUCTION -- 3.2 SIMPLE RANDOM SAMPLING WITHOUT REPLACEMENT -- 3.2.1 Sampling Scheme -- 3.2.2 Estimation of Population Mean and Variance -- 3.2.3 Estimation of Population Covariance -- 3.2.4 Estimation of Population Proportion -- 3.2.5 Estimation of Domain Mean and Total -- 3.3 SIMPLE RANDOM SAMPLING WITH REPLACEMENT -- 3.3.1 Sampling Scheme -- 3.3.2 Estimation of the Population Mean and Variance -- 3.3.3 Estimation of Population Proportion -- 3.3.4 Rao-Blackwellization -- 3.4 INTERVAL ESTIMATION -- 3.4.1 Confidence Intervals for Mean and Proportion -- 3.4.1.1 Large Sample Size -- 3.4.1.2 Small Sample Size -- 3.5 DETERMINATION OF SAMPLE SIZE -- 3.5.1 Consideration of the Cost of a Survey -- 3.5.2 Consideration of the Efficiency of Estimators -- 3.5.2.1 Given Variance -- 3.5.2.2 Given Coefficient of Variation -- 3.5.2.3 Given Margin of Permissible Error. , 3.5.3 Use of Chebyshev Inequality -- 3.6 INVERSE SAMPLING -- 3.6.1 Simple Random Sampling Without Replacement -- 3.6.2 Simple Random Sampling With Replacement -- 3.7 EXERCISES -- 4 - Systematic Sampling -- 4.1 INTRODUCTION -- 4.2 LINEAR SYSTEMATIC SAMPLING -- 4.2.1 Linear Systematic Sampling With N/n=k an Integer -- 4.2.2 Linear Systematic Sampling With N/n=k Not an Integer -- 4.2.3 Estimation of the Population Mean and Its Variance -- 4.2.4 Nonexistence of Unbiased Variance Estimator -- 4.3 EFFICIENCY OF SYSTEMATIC SAMPLING -- 4.3.1 Comparison With Simple Random Sampling -- 4.3.2 Comparison With Stratified Sampling -- 4.3.3 Random Arrangement of Units -- 4.3.4 Population With Linear Trend -- 4.3.4.1 End Corrections -- 4.3.4.2 Balanced Systematic Sampling -- 4.3.5 Population With Periodic Variation -- 4.3.6 Autocorrelated Population -- 4.4 LINEAR SYSTEMATIC SAMPLING USING FRACTIONAL INTERVAL -- 4.5 CIRCULAR SYSTEMATIC SAMPLING -- 4.5.1 Circular Systematic Sampling With k=N/n as an Integer -- 4.5.2 Circular Systematic Sampling With N/n is Not an Integer -- 4.6 VARIANCE ESTIMATION -- 4.6.1 Single Systematic Sample -- 4.6.1.1 Random Arrangements of Units -- 4.6.1.2 Stratified Sampling With One Unit Per Stratum -- 4.6.1.3 Presence of Linear Trend -- 4.6.1.4 Presence of Autocorrelation Between Successive Units -- 4.6.1.5 Splitting of a Systematic Sample -- 4.6.2 Several Systematic Samples -- 4.7 TWO-DIMENSIONAL SYSTEMATIC SAMPLING -- 4.8 EXERCISES -- 5 - Unequal Probability Sampling -- 5.1 INTRODUCTION -- 5.2 PROBABILITY PROPORTIONAL TO SIZE WITH REPLACEMENT SAMPLING SCHEME -- 5.2.1 Cumulative Total Method -- 5.2.2 Lahiri's Method -- 5.2.3 Hansen-Hurwitz Estimator and its Variance -- 5.2.4 Rao-Blackwellization -- 5.3 PROBABILITY PROPORTIONAL TO SIZE WITHOUT REPLACEMENT SAMPLING SCHEME -- 5.3.1 Raj's Estimator and its Variance -- 5.3.2 Rao-Blackwellization. , 5.3.2.1 Murthy's Estimator -- 5.4 INCLUSION PROBABILITY PROPORTIONAL TO MEASURE OF SIZE SAMPLING SCHEME -- 5.4.1 Inclusion Probability Proportional to Measure of Size Sampling With n=2 -- 5.4.1.1 Brewer's Sampling Scheme -- 5.4.1.2 Durbin's Sampling Scheme -- 5.4.1.3 Hanurav's Sampling Scheme -- 5.4.2 Inclusion Probability Proportional to Measure of Size Sampling with n 2 -- 5.4.2.1 Lahiri-Midzuno-Sen Sampling Design -- 5.4.2.2 Probability Proportionate to Size Systematic Sampling Scheme -- 5.4.2.3 Sampford's Sampling Scheme -- 5.4.2.3.1 Comparison of Efficiency -- 5.4.2.4 Poisson (or Bernoulli) Sampling -- 5.4.2.5 Use of Combinatorics -- 5.4.2.6 The Nearest Proportional to Size Sampling -- 5.5 PROBABILITY PROPORTIONAL TO AGGREGATE SIZE WITHOUT REPLACEMENT -- 5.6 RAO-HARTLEY-COCHRAN SAMPLING SCHEME -- 5.7 COMPARISON OF UNEQUAL (VARYING) PROBABILITY SAMPLING DESIGNS -- 5.8 EXERCISES -- 6 - Inference Under Superpopulation Model -- 6.1 INTRODUCTION -- 6.2 DEFINITIONS -- 6.2.1 Sampling Strategy -- 6.2.2 Noninformative Sampling Design -- 6.2.3 Design-Unbiased (or p-Unbiased) Estimator -- 6.2.4 Model-Unbiased (or ξ-Unbiased) Estimator -- 6.2.5 Model Design-Unbiased (or pξ-Unbiased) Estimator -- 6.2.6 Design-Based Inference -- 6.2.7 Model-Based Inference -- 6.2.8 Model-Assisted Inference -- 6.2.9 Optimal Estimator -- 6.2.10 Optimal Strategy -- 6.3 MODEL-ASSISTED INFERENCE -- 6.3.1 Optimal Design-Unbiased Predictors -- 6.3.1.1 Product Measure Model -- 6.3.1.2 Equicorrelation Model -- 6.3.1.3 Transformation Model -- 6.3.2 Optimal Model Design-Unbiased Prediction -- 6.3.3 Exchangeable Model -- 6.3.4 Random Permutation Model -- 6.4 MODEL-BASED INFERENCE -- 6.4.1 Optimal Model-Unbiased Prediction -- 6.4.1.1 Product Measure Model -- 6.4.1.2 Transformation Model -- 6.4.1.3 Multiple Regression Model -- 6.5 ROBUSTNESS OF DESIGNS AND PREDICTORS. , 6.5.1 Robustness of Predictors -- 6.5.2 Balanced Sampling Design -- 6.5.3 Polynomial Regression Model -- 6.5.4 Balanced Sample of Order k -- 6.5.5 Optimality of Balanced Sampling -- 6.6 BAYESIAN INFERENCE -- 6.6.1 Bayes Estimator -- 6.7 COMPARISON OF STRATEGIES UNDER SUPERPOPULATION MODELS -- 6.7.1 Hansen-Hurwitz Strategy With Others -- 6.7.2 Horvitz-Thompson and Rao-Hartley-Cochran Strategy -- 6.7.3 Horvitz-Thompson and Lahiri-Midzuno-Sen Strategy -- 6.7.4 Rao-Hartley-Cochran and Lahiri-Midzuno-Sen Strategy -- 6.8 DISCUSSIONS -- 6.9 EXERCISES -- 7 - Stratified Sampling -- 7.1 INTRODUCTION -- 7.2 DEFINITION OF STRATIFIED SAMPLING -- 7.3 ADVANTAGES OF STRATIFIED SAMPLING -- 7.4 ESTIMATION PROCEDURE -- 7.4.1 Estimation of Population Mean -- 7.4.1.1 Arbitrary Fixed Sample Size Design -- 7.4.1.2 Simple Random Sampling Without Replacement -- 7.4.1.3 Probability Proportional to Size With Replacement Sampling -- 7.4.1.4 Simple Random Sampling With Replacement -- 7.4.2 Estimation of Population Proportion -- 7.4.2.1 Simple Random Sampling Without Replacement -- 7.4.2.2 Simple Random Sampling With Replacement -- 7.4.3 Interval Estimation -- 7.5 ALLOCATION OF SAMPLE SIZE -- 7.5.1 Optimum Allocation for Fixed Cost -- 7.5.2 Optimum Allocation for Fixed Variance -- 7.5.3 Simple Random Sampling Without Replacement -- 7.5.4 Simple Random Sampling With Replacement -- 7.5.5 Probability Proportional to Size With Replacement Sampling -- 7.5.6 Neyman Optimum Allocation -- 7.5.7 Proportional Allocation -- 7.6 COMPARISON BETWEEN STRATIFIED AND UNSTRATIFIED SAMPLING -- 7.6.1 Simple Random Sampling Without Replacement -- 7.6.2 Probability Proportional to Size With Replacement Sampling -- 7.6.3 Inclusion Probability Proportional to Size Sampling Scheme -- 7.7 CONSTRUCTION OF STRATA -- 7.7.1 Optimum Points of Stratification -- 7.7.1.1 Proportional Allocation. , 7.7.1.2 Optimum Allocation.

Additional Edition: ISBN 0-12-811848-2

Additional Edition: ISBN 0-12-811897-0

Language: English

UID:

Format: 1 Online-Ressource (xxvii, 899 Seiten) : , Diagramme.

ISBN: 978-0-12-811897-9

Additional Edition: Erscheint auch als Druck-Ausgabe, Paperback ISBN 978-0-12-811848-1

Language: English

Keywords: Stichprobe

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