Statistical Theory: A Concise Introduction

"Designed for a one-semester advanced undergraduate or graduate course, Statistical Theory: A Concise Introduction clearly explains the underlying ideas and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, 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, this student-oriented, self-contained book 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 detailedtechnical mathematical and probabilistic arguments. Chapters and sections marked by asterisks contain more advanced topics and may be omitted. A special chapter on linear models shows how the main theoretical concepts can be applied to the well-known andfrequently used statistical tool of linear regression.Requiring no heavy calculus, simple questions throughout the text help students check their understanding of the material. Each chapter also includes a set of exercises that range in level of difficulty"--
"Preface This book is intended as a textbook for a one-term course in statistical theory for advanced undergraduates in statistics, mathematics or other related fields although at least parts of it may be useful for graduates as well. Although there exist many good books on the topic, having taught a one-term Statistical Theory course during the years we felt that it is somewhat hard to recommend a particular one as a proper textbook to undergraduate students in statistics. Some of the existing textbookswith a primary focus on rigorous formalism, in our view, do not explain sufficiently clearly the underlying ideas and principles of the main statistical concepts, and are more suitable for graduates. Some others are "all-inclusive" textbooks that includea variety of topics in statistics that make them "too heavy" for a one-term course in statistical theory. Our main motivation was to propose a more "student-oriented" self-contained textbook designed for a one-term course on statistical theory that wouldintroduce basic statistical concepts first on a clear intuitive level with illustrative examples in addition to the (necessary!) formal definitions, theorems and proofs. It is based on our lecture notes. We tried to keep a proper balance between the clarity and rigorousness of exposition. In a few cases we preferred to present a "sketched" version of a proof explaining its main ideas or even to give it up at all rather then to follow detailed technical mathematical and probabilistic arguments. The interested reader can complete those proofs from other existing books on mathematical statistics (see the bibliography)"--