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.
This first volume presents fundamental, classical statistical concepts at the doctorate level without using measure theory. 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 includes in-depth examples throughout as well as many exercises at the end of each chapter.
"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
