Mathematical statistics
著者
書誌事項
Mathematical statistics
（Springer texts in statistics）
Springer, c1999
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注記
Includes bibliographical references and indexes
内容説明・目次
内容説明
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 the classical results that are typically covered in a textbook of a similar level, this book introduces some topics in modern statistical theory that have been developed in recent years, such as Markov chain Monte Carlo, quasi-likelihoods, empirical likelihoods, statistical functionals, generalized estimation equations, the jackknife, and the bootstrap. Jun Shao is Professor of Statistics at the University of Wisconsin, Madison.
目次
Probability Theory.- Fundamentals of Statistics.- Unbiased Estimation.- Estimation in Parametric Models.- Estimation in Nonparametric Models.- Hypothesis Tests.- Confidence Sets.
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