Konishi / Kitagawa Information Criteria and Statistical Modeling

1. Auflage 2007
ISBN: 978-0-387-71887-3
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 276 Seiten

Statistical modeling is a critical tool in scientific research. This book provides comprehensive explanations of the concepts and philosophy of statistical modeling, together with a wide range of practical and numerical examples. The authors expect this work to be of great value not just to statisticians but also to researchers and practitioners in various fields of research such as information science, computer science, engineering, bioinformatics, economics, marketing and environmental science. It's a crucial area of study, as statistical models are used to understand phenomena with uncertainty and to determine the structure of complex systems. They're also used to control such systems, as well as to make reliable predictions in various natural and social science fields.

Autoren/Hrsg.

Konishi, Sadanori

Kitagawa, Genshiro

Inhaltsverzeichnis

1;Preface;6
2;Contents;9
3;1 Concept of Statistical Modeling;13
3.1;1.1 Role of Statistical Models;13
3.2;1.2 Constructing Statistical Models;16
3.3;1.3 Organization of This Book;19
4;2 Statistical Models;21
4.1;2.1 Modeling of Probabilistic Events and Statistical Models;21
4.2;2.2 Probability Distribution Models;22
4.3;2.3 Conditional Distribution Models;29
5;3 Information Criterion;41
5.1;3.1 Kullback–Leibler Information;41
5.2;3.2 Expected Log-Likelihood and Corresponding Estimator;47
5.3;3.3 Maximum Likelihood Method and Maximum Likelihood Estimators;49
5.4;3.4 Information Criterion AIC;63
5.5;Xn;;675.6;3.5 Properties of MAICE81
6;4 Statistical Modeling by AIC;87
6.1;4.1 Checking the Equality of Two Discrete Distributions;87
6.2;4.2 Determining the Bin Size of a Histogram;89
6.3;4.3 Equality of the Means and/or the Variances of Normal Distributions;91
6.4;4.4 Variable Selection for Regression Model;96
6.5;4.5 Generalized Linear Models;100
6.6;4.6 Selection of Order of Autoregressive Model;104
6.7;4.7 Detection of Structural Changes;108
6.8;4.8 Comparison of Shapes of Distributions;113
6.9;4.9 Selection of Box–Cox Transformations;116
7;5 Generalized Information Criterion (GIC);119
7.1;5.1 Approach Based on Statistical Functionals;119
7.2;5.2 Generalized Information Criterion (GIC);130
8;6 Statistical Modeling by GIC;151
8.1;6.1 Nonlinear Regression Modeling via Basis Expansions;151
8.2;6.2 Basis Functions;155
8.3;6.3 Logistic Regression Models for Discrete Data;161
8.4;6.4 Logistic Discriminant Analysis;168
8.5;6.5 Penalized Least Squares Methods;172
8.6;6.6 Effective Number of Parameters;174
9;7 Theoretical Development and Asymptotic Properties of the GIC;178
9.1;7.1 Derivation of the GIC;178
9.2;7.2 Asymptotic Properties and Higher-Order Bias Correction;187
10;8 Bootstrap Information Criterion;197
10.1;8.1 Bootstrap Method;197
10.2;8.2 Bootstrap Information Criterion;202
10.3;8.3 Variance Reduction Method;205
10.4;8.4 Applications of Bootstrap Information Criterion;216
11;9 Bayesian Information Criteria;220
11.1;9.1 Bayesian Model Evaluation Criterion (BIC);220
11.2;9.2 Akaike’s Bayesian Information Criterion (ABIC);231
11.3;9.3 Bayesian Predictive Distributions;233
11.4;9.4 Bayesian Predictive Distributions by Laplace Approximation;240
11.5;9.5 Deviance Information Criterion (DIC);245
12;10 Various Model Evaluation Criteria;247
12.1;10.1 Cross-Validation;247
12.2;10.2 Final Prediction Error (FPE);255
12.3;10.3 Mallows’ Cp;259
12.4;10.4 Hannan–Quinn’s Criterion;261
12.5;10.5 ICOMP;262
13;References;263
14;Index;276