Introductory Statistical Inference

This gracefully organized text reveals the rigorous theory of probability and statistical inference in the style of a tutorial using worked examples exercises figures tables and computer simulations to develop and illustrate concepts. Drills and boxed summaries emphasize and reinforce important ideas and special techniques. Beginning with a review of the basic concepts and methods in probability theory moments and moment generating functions the author moves to more intricate topics. Introductory Statistical Inference studies multivariate random variables exponential families of distributions and standard probability inequalities. It develops the Helmert transformation for normal distributions introduces the notions of convergence and spotlights the central limit theorems. Coverage highlights sampling distributions Basu's theorem Rao-Blackwellization and the Cramér-Rao inequality. The text also provides in-depth coverage of Lehmann-Scheffé theorems focuses on tests of hypotheses describes Bayesian methods and the Bayes' estimator and develops large-sample inference. The author provides a historical context for statistics and statistical discoveries and answers to a majority of the end-of-chapter exercises. Designed primarily for a one-semester first-year graduate course in probability and statistical inference this text serves readers from varied backgrounds ranging from engineering economics agriculture and bioscience to finance financial mathematics operations and information management and psychology.