This graduate textbook covers those topics in statistical theory essential for 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, while the second introduces some fundamental concepts in statistical decision theory and inference. The remaining chapters contain detailed studies on such important topics as: 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 this 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.

Inhalt

Probability Theory Fundamentals of Statistics Unbiased Estimation Estimation in Parametric Models Estimation in Nonparametric Models Hypothesis Tests Confidence Sets