Kooperativer Bibliotheksverbund

UID:

Format: XXI, 455 S. : graph. Darst.

Edition: Repr.

ISBN: 981-02-3242-X

Language: English

Subjects: Mathematics

Keywords: Regressionsanalyse ; Zeitreihe ; Zeitreihenanalyse

UID:

Format: XXI, 455 S. , graph. Darst.

ISBN: 981023242X

Language: English

Subjects: Mathematics

Keywords: Zeitreihenanalyse ; Regressionsanalyse ; Zeitreihe

URL: Inhaltsverzeichnis

URL: Inhaltstext

UID:

Format: 1 online resource (479 p.)

Edition: 1st ed.

ISBN: 981-238-545-2

Content: This important book describes procedures for selecting a model from a large set of competing statistical models. It includes model selection techniques for univariate and multivariate regression models, univariate and multivariate autoregressive models, nonparametric (including wavelets) and semiparametric regression models, and quasi-likelihood and robust regression models. Information-based model selection criteria are discussed, and small sample and asymptotic properties are presented. The book also provides examples and large scale simulation studies comparing the performances of informati

Note: Description based upon print version of record. , Contents; Preface; List of Tables; Chapter 1 Introduction; 1.1. Background; 1.1.1. Historical Review; 1.1.2. Eficient Criteria; 1.1.3. Consistent Criteria; 1.2. Overview; 1.2.1. Distributions; 1.2.2. Model Notation; 1.2.3. Discrepancy and Distance Measures; 1.2.4. Eficiency under Kullback-Leibler and L2; 1.2.5. Overfitting and Underfitting; 1.3. Layout; 1.4. Topics Not Covered; Chapter 2 The Univariate Regression Model; 2.1. Model Description; 2.1.1. Model Structure and Notation; 2.1.2. Distance Measures; 2.2. Derivations of the Foundation Model Selection Criteria , 2.3. Moments of Model Selection Criteria2.3.1. AIC and AICc; 2.3.2. FPE and Cp; 2.3.3. SIC and HQ; 2.3.4. Adjusted R2, R2adj; 2.4. Signal-to-noise Corrected Variants; 2.4.1. AICu; 2.4.2. FPEu; 2.4.3. HQu; 2.5. Overfitting; 2.5.1. Small-sample Probabilities of Overfitting; 2.5.2. Asymptotic Probabilities of Overfitting; 2.5.3. Small-sample Signal-to-noise Ratios; 2.5.4. Asymptotic Signal-to-noise Ratios; 2.6. Small-sample Underfitting; 2.6.1. Distributional Review; 2.6.2. Expectations of L2 and Kullback-Leibler Distance; 2.6.3. Expected Values for Two Special Case Models , 2.6.4. Signal-to-noise Ratios for Two Special Case Models2.6.5. Small-sample Probabilities for Two Special Case Models; 2.7. Random X Regression and Monte Carlo Study; 2.8. Summary; Appendix 2A. Distributional Results in the Central Case; Appendix 2B. Proofs of Theorems 2.1 to 2.6; Appendix 2C. Small-sample and Asymptotic Properties; Appendix 2D. Moments of the Noncentral X2; Chapter 3 The Univariate Autoregressive Model; 3.1. Model Description; 3.1.1. Autoregressive Models; 3.1.2. Distance Measures; 3.2. Selected Derivations of Model Selection Criteria; 3.2.1. AIC; 3.2.2. AICc; 3.2.3. AICu , 3.2.4. FPE3.2.5. FPEu; 3.2.6. Cp; 3.2.7. SIC; 3.2.8. HQ; 3.2.9. HQc; 3.3. Small-sample Signal-to-noise Ratios; 3.4. Overfitting; 3.4.1. Small-sample Probabilities of Overfitting; 3.4.2. Asymptotic Probabilities of Overfitting; 3.4.3. Small-sample Signal-to-noise Ratios; 3.4.4. Asymptotic Signal-to-noise Ratios; 3.5. Underfitting for Two Special Case Models; 3.5.1. Expected Values for Two Special Case Models; 3.5.2. Signal-to-noise Ratios for Two Special Case Models; 3.5.3. Probabilities for Two Special Case Models; 3.6. Autoregressive Monte Carlo Study , 3.7. Moving Average MA(1) Misspecified as Autoregressive Models3.7.1. Two Special Case MA(1) Models; 3.7.2. Model and Distance Measure Definitions; 3.7.3. Expected Values for Two Special Case Models; 3.7.4. Masspecified MA(1) Monte Carlo study; 3.8. Multistep Forecasting Models; 9.8.1. Kullback-Leibler Discrepancy for Multistep; 3.8.2. AICcm, AICm, and FPEm; 3.8.3. Multistep Monte Carlo Study; 3.9. Summary; Appendix 3A. Distributional Results in the Central Case; Appendix 3B. Small-sample Probabilities of Overfitting; Appendix 3C. Asymptotic Results , Chapter 4 The Multivariate Regression Model , English

Additional Edition: ISBN 981-02-3242-X

Language: English

UID:

Format: 1 online resource (341 p.)

Edition: Reprint 2011

ISBN: 9783110883596 , 9783110637199

Series Statement: De Gruyter Proceedings in Mathematics ; Conference B

Note: I-X -- , Section 1: Probability Theory -- , Asymptotic normality of the solutions of the multidimensional Burger equation with random data -- , Multivariate minimal moments -- , A geometric approach to the Gaussian law -- , Axiomatic foundations of the theory of interval-probability -- , Section 2: Probabilistic Expert Systems -- , AKTALYST-a causal probabilistic expert system for stock market analysis -- , Focusing and learning in possibilistic dependency networks -- , A Bayesian approach to imprecision in belief nets -- , Causal probabilistic networks and their application to metabolic processes -- , Maximum likelihood estimation and learning in large systems -- , Section 3: Statistical Decision Theory -- , An independence transformation in decision theory -- , Set-valued decision functions and reduction of dimensionality by selection of variables -- , Empirical Bayes two-stage procedures for selecting the best normal population compared with a control -- , Four concepts in decision theory based on order completeness of L1 -- , Admissibility conditions for estimators of exponential type functions -- , Section 4: Simulation and Resampling -- , Variance estimation in generalized linear models using the bootstrap -- , Using the jackknife in the analysis of contingency tables for the estimation of the common odds ratio -- , A certain robustness for tests in the case of discrete distributions -- , Section 5: Linear Models and Design of Experiments -- , Estimating linear measurement error models via M-estimation -- , Bayesian generalized errors in variables (GEIV) models for censored regressions -- , Experimental design for linear models with higher interaction terms -- , Missing values in regression: mixed and weighted mixed estmation -- , Section 9: General Methods and Applications -- , The amount of information and the bound for the order of consistency for a location parameter family of densities -- , An ordinal model for constructing a quadratic objective function of economic policy -- , Selection of prognostic factors concerning prospective studies with censored observations: comparison of Cox-regression and CART-method -- , Alphabetical List of Contributors -- , Author Index , Issued also in print. , Mode of access: Internet via World Wide Web. , In English.

In: DGBA Mathematics - 1990 - 1999, De Gruyter, 9783110637199

Additional Edition: ISBN 9783110144123

Language: English

Subjects: Mathematics

DOI: 10.1515/9783110883596

URL: https://doi.org/10.1515/9783110883596

URL: https://www.degruyter.com/isbn/9783110883596

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