Mathematical Statistics Basic Ideas and Selected Topics Volume II

Description

Mathematical Statistics: Basic Ideas and Selected Topics, Volume II presents important statistical concepts, methods, and tools not covered in the authors’ previous volume. This second volume focuses on inference in non- and semiparametric models. It not only reexamines the procedures introduced in the first volume from a more sophisticated point of view but also addresses new problems originating from the analysis of estimation of functions and other complex decision procedures and large-scale data analysis. The book covers asymptotic efficiency in semiparametric models from the Le Cam and Fisherian points of view as well as some finite sample size optimality criteria based on Lehmann–Scheffé theory. It develops the theory of semiparametric maximum likelihood estimation with applications to areas such as survival analysis. It also discusses methods of inference based on sieve models and asymptotic testing theory. The remainder of the book is devoted to model and variable selection, Monte Carlo methods, nonparametric curve estimation, and prediction, classification, and machine learning topics. The necessary background material is included in an appendix. Using the tools and methods developed in this textbook, students will be ready for advanced research in modern statistics. Numerous examples illustrate statistical modeling and inference concepts while end-of-chapter problems reinforce elementary concepts and introduce important new topics. As in Volume I, measure theory is not required for understanding. The solutions to exercises for Volume II are included in the back of the book. Check out Volume I for fundamental, classical statistical concepts leading to the material in this volume. Front Cover......Page 1 Dedication......Page 9 CONTENTS......Page 11 PREFACE TO THE 2015 EDITION......Page 17 Chapter I - INTRODUCTION AND EXAMPLES......Page 23 Chapter 7 - TOOLS FOR ASYMPTOTIC ANALYSIS......Page 43 Chapter 8 - DISTRIBUTION-FREE, UNBIASED, AND EQUIVARIANT PROCEDURES......Page 95 Chapter 9 - INFERENCE IN SEMIPARAMETRIC MODELS......Page 147 Chapter 10 - MONTE CARLO METHODS......Page 233 Chapter 11 - NONPARAMETRIC INFERENCE FOR FUNCTIONS OF ONE VARIABLE......Page 287 Chapter 12 - PREDICTION AND MACHINE LEARNING......Page 329 Appendix D - SOME AUXILIARY RESULTS......Page 421 Appendix E - SOLUTIONS FOR VOLUME II......Page 445 REFERENCES......Page 459 Insert 1......Page 477 Back Cover......Page 479