Statistical Theory Av Felix Abramovich, Ya'Acov Ritov

Designed for a one-semester advanced undergraduate or graduate statistical theory course, Statistical Theory: A Concise Introduction, Second Edition clearly explains the underlying ideas, mathematics, and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, linear models, nonparametric statistics, and elements of decision theory. It introduces these topics on a clear intuitive level using illustrative examples in addition to the formal definitions, theorems, and proofs.Based on the authors’ lecture notes, the book is self-contained, which maintains a proper balance between the clarity and rigor of exposition. In a few cases, the authors present a "sketched" version of a proof, explaining its main ideas rather than giving detailed technical mathematical and probabilistic arguments. Features:Second edition has been updated with a new chapter on Nonparametric Estimation; a significant update to the chapter on Statistical Decision Theory; and other updates throughoutNo requirement for heavy calculus, and simple questions throughout the text help students check their understanding of the materialEach chapter also includes a set of exercises that range in level of difficultySelf-contained, and can be used by the students to understand the theoryChapters and sections marked by asterisks contain more advanced topics and may be omittedSpecial chapters on linear models and nonparametric statistics show how the main theoretical concepts can be applied to well-known and frequently used statistical toolsThe primary audience for the book is students who want to understand the theoretical basis of mathematical statistics—either advanced undergraduate or graduate students. It will also be an excellent reference for researchers from statistics and other quantitative disciplines.