Essential Statistical Inference: Theory and Methods

ISBN-13: 9781489987938 / Angielski / Miękka / 2015 / 568 str.

Dennis D. Boos; Leonard a. Stefanski

Opis

This book is for students and researchers who have had a first year graduate level mathematicalstatistics course. It covers classical likelihood, Bayesian, and permutation inference;an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large numberof examples and problems.

An important goal has been to make the topics accessible to a wide audience, with little overt relianceon measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimationand testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology.

Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State.Their research has been eclectic, often with a robustness angle, although Stefanski is also known forresearch concentrated on measurement error, including a co-authored book on non-linear measurementerror models. In recent years the authors have jointly worked on variable selection methods. "

Recenzje

"The book is aimed at Ph.D. students in statistics who have already taken some basic graduate level Mathematical Statistics course. It succeeded in being at the perfect level to be beneficial to every statistic student. To the theoretically minded student it brings an exposure to how applications motivates statistics while to the applied student it gives theoretically motivated understanding of why the methods work. It also contains explanation of numerical methods including some implementation in R." (Jan Hannig, Journal of Agricultural, Biological, and Environmental Statistics, February, 2015)

"Throughout this well written textbook, the authors engage the reader by marrying historical descriptions of central questions in classical statistics with modern techniques and approaches. ... The exercises at the end of each chapter are insightful and ideal for homework assignments. This book will surely become a widely used text for second-year graduate courses on inference, as well as an invaluable reference for statistical researchers." (Russell T. Shinohara, The American Statistician, Vol. 68 (3), August, 2014)

"Essential statistical inference by Boos and Stefanski is an excellent book with appeal to advanced undergraduate and graduate students as well as researchers. ... An appropriate list of references is given at the end of the book. ... It is a welcome addition to the overcrowded statistical market and can be easily ranked as one of the best books, if not the best, on statistical inference (theory and methods)." (D. V. Chopra, Mathematical Reviews, August, 2014)

"This book is organised in five parts where the authors extensively present the roles of modelling in statistical inference (part 1), likelihood based methods (part 2), large sample approximations (part 3), methods for mis-specified likelihoods and partially defined models (part 4), and concludes with computation based methods (part 5). ... The book is written in an accessible manner for both undergraduates and researchers and it is a valuable resource and starting point for statistical inference." (Irina Ioana Mohorianu, zbMATH, Vol. 1276, 2014)

Spis treści

​ ​Roles of Modeling in Statistical Inference.- Likelihood Construction and Estimation.- Likelihood-Based Tests and Confidence Regions.- Bayesian Inference.- Large Sample Theory: The Basics.- Large Sample Results for Likelihood-Based Methods.- M-Estimation (Estimating Equations).- Hypothesis Tests under Misspecification and Relaxed Assumptions​.- Monte Carlo Simulation Studies​.- Jackknife.- Bootstrap.- Permutation and Rank Tests.- Appendix: Derivative Notation and Formulas.- References.- Author Index.- Example Index​.- R-code Index.- Subject Index.

O autorze

Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods.