Format:
Online-Ressource (XXXV, 507 p, online resource)
ISBN:
9781461201038
Series Statement:
Statistics for Industry and Technology
Content:
I: History and Fundamentals -- 1 Karl Pearson and the Chi-Squared Test -- 2 Karl Pearson Chi-Square Test—The Dawn of Statistical Inference -- 3 Approximate Models -- II: Chi-Squared Test -- 4 Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic -- 5 Statistical Tests for Normal Family in Presence of Outlying Observations -- 6 Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files -- III: Goodness-of-Fit Tests for Parametric Distributions -- 7 Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited -- 8 A Test for Exponentiality Based on Spacings for Progressively Type-II Censored Data -- 9 Goodness-of-Fit Statistics for the Exponential Distribution When the Data are Grouped -- 10 Characterization Theorems and Goodness-of-Fit Tests -- 11 Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data -- IV: Regression and Goodness-of-Fit Tests -- 12 Gibbs Regression and a Test of Goodness-of-Fit -- 13 A CLT for the L_2 Norm of the Regression Estimators Under ?-Mixing: Application to G-O-F Tests -- 14 Testing the Goodness-of-Fit of a Linear Model in Nonparametric Regression -- 15 A New Test of Linear Hypothesis in Regression -- V: Goodness-of-Fit Tests in Survival Analysis and Relability -- 16 Inference in Extensions of the Cox Model for Heterogeneous Populations -- 17 Assumptions of a Latent Survival Model -- 18 Goodness-of-Fit Testing for the Cox Proportional Hazards Model -- 19 A New Family of Multivariate Distributions for Survival Data -- 20 Discrimination Index, the Area Under the ROC Curve -- 21 Goodness-of-Fit Tests for Accelerated Life Models -- VI: Graphical Methods and General Goodness-of-Fit Tests -- 22 Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards -- 23 Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plot -- 24 Orthogonal Expansions and Distinction Between Logistic and Normal -- 25 Functional Tests of Fit -- 26 Quasi Most Powerful Invariant Tests of Goodness-of-Fit -- VII: Model Validity in Quality of Life -- 27 Test of Monotonicity for the Rasch Model -- 28 Validation of Model Assumptions in Quality of Life Measurements -- VIII: Tests of Hypotheses and Estimation with Applications -- 29 One-Sided Hypotheses in a Multinomial Model -- 30 A Depth Test for Symmetry Peter -- 31 Adaptive Combination of Tests -- 32 Partially Parametric Testing -- 33 Exact Nonparametric Two-Sample Homogeneity Tests -- 34 Power Comparisons of Some Nonparametric Tests for Lattice Ordered Alternatives in Two-Factor Experiments -- 35 Tests of Independence with Exponential Marginals -- 36 Testing Problem for Increasing Function in a Model with Infinite Dimensional Nuisance Parameter -- 37 The Concept of Generalized Asymptotic Deficiency and its Application to the Minimum Discrepancy Estimation.
Content:
The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real-life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.
Note:
Preface -- Contributors -- List of Tables -- List of Figures -- Part I. History and Fundamentals -- Karl Pearson and the Chi-Squared Test -- Karl Pearson Chi-Square Test-The Dawn of Statistical Inference -- Approximate Models -- Part II. Chi-Squared Test -- Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic -- Statistical Tests for Normal Family in Presence of Outlying Observations -- Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files -- Part III. Goodness-of-Fit Tests for Parametric Distributions -- Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited -- A Test for Exponentiality Based on Spacings for Progressively Type II Censored Data -- Goodness-of-Fit Statistics for the Exponential Distribution When the Data are Grouped -- Characterization Theorems and Goodness-of-Fit Tests -- Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data -- Part IV. Regression and Goodness-of-Fit Tests -- Gibbs Regression and a Test of Goodness-of-Fit -- A CLT for the L_2 Norm of the Regression Estimators Under alpha-Mixing: Application to G-O-F Tests -- Testing the Goodness-of-Fit of a Linear Model in Nonparametric Regression -- A New Test of Linear Hypothesis in Regression -- Part V. Goodness-of-Fit Tests in Survival Analysis and Reliability -- Inference in Extensions of the Cox Model for Heterogeneous Populations -- Assumptions of a Latent Survival Model -- Goodness-of-Fit Testing of the Cox Proportional Hazards Model -- A New Family of Multivariate Distributions for Survival Data -- Discrimination Index, the Area Under to ROC Curve -- Goodness-of-Fit Tests for Accelerated Life Models -- Part VI. Graphic Methods and General Goodness-of-Fit Tests -- Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards -- Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plots -- Orthogonal Expansions and Distinction Between Logistic and Normal -- Functional Tests of Fit -- Quasi Most Powerful Invariant Tests of Goodness-of-Fit -- Part VII. Model Validity in Quality of Life -- Test of Monotonicity for the Rasch Model -- Validation of Model Assumptions in Quality of Life Measurements -- Part VIII. Tests of Hypotheses and Estimation with Applications -- One-Sided Hypotheses in a Multinomial Model -- A Depth Test for Symmetry -- Adaptive Combination of Tests -- Partially Parametric Testing -- Exact Nonparametric Two-Sample Homogeneity Tests -- Power Comparisons of Some Nonparametric Tests for Lattice Ordered Alternatives in Two-Factor Experiments -- Tests of Independence with Exponential Marginals -- Testing Problem for Increasing Function in a Model with Infinite Dimensional Nuisance Parameter -- The Concept of Generalized Asymptotic Deficiency and its Application to the Minimum Discrepancy Estimation -- Index .
Additional Edition:
ISBN 9781461266136
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 978-146-126-613-6
Language:
English
DOI:
10.1007/978-1-4612-0103-8
URL:
Volltext
(lizenzpflichtig)
Author information:
Nikulin, Michail S.
