Ebook: Mathematical Statistics

This graduate textbook covers topics in statistical theory essential for graduate students preparing for work on a Ph.D. degree in statistics. The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics. The second chapter introduces some fundamental concepts in statistical decision theory and inference. Chapters 3-7 contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets. A large number of exercises in each chapter provide not only practice problems for students, but also many additional results.

In addition to improving the presentation, the new edition makes Chapter 1 a self-contained chapter for probability theory with emphasis in statistics. Added topics include useful moment inequalities, more discussions of moment generating and characteristic functions, conditional independence, Markov chains, martingales, Edgeworth and Cornish-Fisher expansions, and proofs to many key theorems such as the dominated convergence theorem, monotone convergence theorem, uniqueness theorem, continuity theorem, law of large numbers, and central limit theorem. A new section in Chapter 5 introduces semiparametric models, and a number of new exercises were added to each chapter.

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This graduate textbook covers a huge range of essential topics in statistical theory.

This new edition has been revised and updated and in this fourth printing, errors have been ironed out.

The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics.

The second chapter introduces some fundamental concepts in statistical decision theory and inference.

Subsequent chapters contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets.

A large number of exercises in each chapter provide not only practice problems for students, but also many additional results.

In addition to improving the presentation, the new edition makes Chapter 1 a self-contained chapter for probability theory with emphasis in statistics.

Added topics include useful moment inequalities, more discussions of moment generating and characteristic functions, and proofs to many key theorems such as the dominated convergence theorem.

---

This graduate textbook covers a huge range of essential topics in statistical theory.

This new edition has been revised and updated and in this fourth printing, errors have been ironed out.

The first chapter provides a quick overview of concepts and results in measure-theoretic probability theory that are useful in statistics.

The second chapter introduces some fundamental concepts in statistical decision theory and inference.

Subsequent chapters contain detailed studies on some important topics: unbiased estimation, parametric estimation, nonparametric estimation, hypothesis testing, and confidence sets.

A large number of exercises in each chapter provide not only practice problems for students, but also many additional results.

In addition to improving the presentation, the new edition makes Chapter 1 a self-contained chapter for probability theory with emphasis in statistics.

Added topics include useful moment inequalities, more discussions of moment generating and characteristic functions, and proofs to many key theorems such as the dominated convergence theorem.

Content:
Front Matter....Pages i-xvi
Probability Theory....Pages 1-90
Fundamentals of Statistics....Pages 91-160
Unbiased Estimation....Pages 161-230
Estimation in Parametric Models....Pages 231-318
Estimation in Nonparametric Models....Pages 319-392
Hypothesis Tests....Pages 393-470
Confidence Sets....Pages 471-542
Back Matter....Pages 543-593