Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition presents fundamental, classical statistical concepts at the doctorate level. It covers estimation, prediction, testing, confidence sets, Bayesian analysis, and the general approach of decision theory. This edition gives careful proofs of major results and explains how the theory sheds light on the properties of practical methods.
The book first discusses non- and semiparametric models before covering parameters and parametric models. It then offers a detailed treatment of maximum likelihood estimates (MLEs) and examines the theory of testing and confidence regions, including optimality theory for estimation and elementary robustness considerations. It next presents basic asymptotic approximations with one-dimensional parameter models as examples. The book also describes inference in multivariate (multiparameter) models, exploring asymptotic normality and optimality of MLEs, Wald and Rao statistics, generalized linear models, and more.
Mathematical Statistics: Basic Ideas and Selected Topics, Volume II will be published in 2015. It will present important statistical concepts, methods, and tools not covered in Volume I.
Table of Contents
STATISTICAL MODELS, GOALS, AND PERFORMANCE CRITERIA. METHODS OF ESTIMATION. MEASURES OF PERFORMANCE. TESTING AND CONFIDENCE REGIONS. ASYMPTOTIC APPROXIMATIONS. INFERENCE IN THE MULTIPARAMETER CASE. APPENDICES. INDEX.
Peter J. Bickel is a professor emeritus in the Department of Statistics and a professor in the Graduate School at the University of California, Berkeley. Dr. Bickel is a member of the American Academy of Arts and Sciences and the National Academy of Sciences. He has been a Guggenheim Fellow and MacArthur Fellow, a recipient of the COPSS Presidents’ Award, and president of the Bernoulli Society and the Institute of Mathematical Statistics. He holds honorary doctorate degrees from the Hebrew University of Jerusalem and ETH Zurich.
Kjell A. Doksum is a senior scientist in the Department of Statistics at the University of Wisconsin–Madison. His research encompasses the estimation of nonparametric regression and correlation curves, inference for global measures of association in semiparametric and nonparametric settings, the estimation of regression quantiles, statistical modeling and analysis of HIV data, the analysis of financial data, and Bayesian nonparametric inference.
"These methods are clearly explained by two outstanding statistical practitioners. … This book is well supported by the references, increasing its value as a guide through the often difficult world of mathematical statistics. …the authors consider key topics which include asymptotic efficiency in semiparametric models, semiparametric maximum likelihood estimation, proportional hazards regression models and Markov chain Monte Carlo methods."
— Receptos Pharmaceuticals, San Diego, 2016