理论统计（英文版）_Robert，W.Keener 著_9787519226190

　　《理论统计（英文版）》是一本内容简明，结构严谨的理论统计教科书，内容包括自助法、非参数回归、同变估计、经验贝叶斯、序贯设计和分析。
　　《理论统计（英文版）》各章有丰富的习题，解答在附录中提供。读者需具备微积分、线性代数、概率论、数学分析和拓扑等数学基础知识。目次：概率和测度；指数族；风险，充分性，完整性；无偏估计；曲指数族；条件分布；贝叶斯估计；大样本理论；估计方程和大概似值；同变估计；经验贝叶斯法和收缩估计；假设检验；高维优化试验等。

　　This book evolved from my notes for a three-semester sequence of core courses on theoretical statistics for doctoral students at the University of Michigan. When I first started teaching these courses， I used Theory of Poin，t Estimation and Testing Statistical Hypotheses by Lehmann as texts， classic books that have certainly influenced my writings.
　　To appreciate this book students will need a background in advanced cal culus， linear algebra， probability， and some analysis. Some of this material is reviewed in the appendices. And， although the content on statistics is reasonably self-contained， prior knowledge of theoretical and applied statistics will be essential for most readers.
　　In teaching core courses， my philosophy has been to try to expose students to as many of the central theoretical ideas and topics in the discipline as possible. Given the growth of statistics in recent years， such exposition can only be achieved in three semesters by sacrificing depth. Although basic material presented in early chapters of the book is covered carefully， many of the later chapters provide brief introductions to areas that could take a full semester to develop in detail.
　　The role of measure theory in advanced statistics courses deserves careful consideration. Although few students will need great expertise in probability and measure， all should graduate conversant enough with the basics to read and understand research papers in major statistics journals， at least in their areas of specialization. Many， if not most， of these papers will be written using the language of measure theory， if not all of its substance. As a practical matter， to prepare for thesis research many students will want to begin studying advanced methods as soon as possible， often before they have finished a course on measure and probability. In this book I follow an approach that makes such study possible. Chapter 1 introduces probability and measure theory， stating many of the results used most regularly in statistics. Although this material cannot replace an honest graduate course on probability， it gives most students the background and tools they need to read and understand most theoretical derivations in statistics. As we use this material in the rest of the book， I avoid esoteric mathematical details unless they are central to a proper understanding of issues at hand. In addition to the intrinsic value of concepts from measure theory， there are several other advantages to this approach. First， results in the book can be stated precisely and at their proper level of generality， and most of the proofs presented are essentially rigorous. In addition， the use of material from probability， measure theory， and analysis in a statistical context will help students appreciate its value and will motivate some to study and learn probability at a deeper level. Although this approach is a challenge for some students， and may make some statistical issues a bit harder to understand and appreciate， the advantages outweigh these concerns.
　　As a caveat I should mention that some sections and chapters， mainly later in the book， are more technical than most and may not be accessible without a sufficient background in mathematics. This seems unavoidable to me； the topics considered cannot be covered properly otherwise.

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