附註:Includes index.
Cover -- Teacher's Preface -- Table of Contents -- Getting Started -- 1. Structural Models for Data -- 2. Least Squares Methods -- 3. Combinatorial Probability -- 4. Other Probability Models -- 5. Discrete Random Variables I: The Hypergeometric Process -- 6. Discrete Random Variables II: The Bernoulli Process -- 7. Random Vectors and Random Samples -- 8. Maximum Likelihood Estimates for Discrete Models -- 9. Continuous Random Variables I: The Gamma and Beta Families -- 10. Continuous Random Variables II: Expectations and the Normal Family -- 11. Continuous Random Vectors -- 12. Sampling Statistics for the Linear Model -- 13. Representing Distributions -- Hints and Solutions to Certain Exercises.
Includes bibliographical references and index.
摘要:This textbook introduces the mathematical concepts and methods that underlie statistics. The course is unified, in the sense that no prior knowledge of probability theory is assumed; this is developed as needed. The book is committed to a high level of mathematical seriousness; and to an intimate connection with application. Modern methods, such as logistic regression, are introduced; as are unjustly neglected clasical topics, such as elementary asymptotics. The book first develops elementary linear models for measured data and multiplicative models for counted data. Simple probability models for random error follow. The most important famiies of random variables are then studied in detail, emphasizing their interrelationships and their large-sample behavior. Inference, including classical, Bayesian, finite population, and likelihood-based, is introduced as the necessary mathematical tools become available. In teaching style, the book aims to be * mathematically complete: every formula is derived, every theorem proved at the appropriate level * concrete: each new concept is introduced and exemplified by interesting statistical problems; and more abstract concepts appear only gradually * constructive: direct derivations and proofs are preferred * active: students are led to do mathematical statistics, not just to appreciate it, with the assistance of 500 interesting exercises. The text is aimed for the upper undergraduate level, or the beginning Masters program level. It assumes the usual two-year college mathematics sequence, including an introduction to multiple integrals, matrix algebra, and infinite series. George R. Terrell received his degrees from Rice University, where he later taught. Since 1986 he has taught in the Statistics Department of.
