Mathematical statistics : basic ideas and selected topics. Volume I
CALL NO : QA276 B583m 2015
IMPRINT : Boca Raton, Fla. : CRC Press, c2015
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.
- Helps Ph.D. students understand classical statistical concepts without using measure theory
- Offers extensive material on Bayesian models and analysis as well as prediction and k-parameter exponential families
- Analyzes how a coordinate descent algorithm for convex optimization is used to compute MLEs in multiparameter exponential families
- Compares Bayesian and frequentist procedures
- Uses multivariate calculus in an intrinsic way, providing a stepping stone to higher-level topics
- Includes a self-contained appendix on advanced topics from probability theory, with proofs of most statements, problems, and references to the literature
- Contains in-depth examples throughout as well as many exercises at the end of each chapter