Asymptotic Theory of Statistics and Probability (Springer Texts in Statistics)

书籍介绍(英文)

This book is an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. The book has 34 chapters over a wide range of topics, nearly 600 exercises for practice and instruction, and another 300 worked out examples. It also includes a large compendium of 300 useful inequalities on probability, linear algebra, and analysis that are collected together from numerous sources, as an invaluable reference for researchers in statistics, probability, and mathematics.

It can be used as a graduate text, as a versatile research reference, as a source for independent reading on a wide assembly of topics, and as a window to learning the latest developments in contemporary topics. The book is unique in its detailed coverage of fundamental topics such as central limit theorems in numerous setups, likelihood based methods, goodness of fit, higher order asymptotics, as well as of the most modern topics such as the bootstrap, dependent data, Bayesian asymptotics, nonparametric density estimation, mixture models, and multiple testing and false discovery. It provides extensive bibliographic references on all topics that include very recent publications.

这本书是百科全书式的经典治疗以及当代大样本理论，既概率统计问题和处理问题和工具。它是用一个非常清晰的风格，一对有问题的影响和相关的定理的重要性概念性讨论重点。这本书已经超过广泛的议题34章，近600个练习练习和指导，并制定了一个300的例子。它还包括一个300的概率大汇编有用的不等式，线性代数，分析是从多种渠道收集起来，作为一个统计，概率研究人员宝贵的参考和数学。

它可以用来作为毕业文本，作为一个多才多艺的研究参考，作为就广泛的议题集会的独立阅读的来源，并以此为主题的学习当代的最新发展的窗口。这本书具有独特的基本主题的详细报道，例如在许多设置中心极限定理，可能的方法，拟合优度，高阶渐近，以及最现代的议题，例如引导，依靠数据，贝叶斯渐近，非参数密度估计，混合模式，以及多种测试和虚假的发现。它提供了所有的议题，包括最近的出版物广泛的参考书目。