应用统计学丛书·随机域中的极值统计学：理论及应用（英文版） [Extremes in Random Fields A Theory and Its Applications] 下载 mobi epub pdf 电子书 2024

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　　《应用统计学丛书·随机域中的极值统计学：理论及应用（英文版）》可作为概率和统计专业的高级课程或讨论班的教材，也可供相关专家参考。

内容简介

　　《应用统计学丛书·随机域中的极值统计学：理论及应用（英文版）》以通俗易懂的方式介绍了随机域中研究极值分布的某些新颖而有效的方法。全书分成两部分。第一部分总结随机域中极值的尾概率的渐近估计的一般方法。结合一些简单或者基本的例子，全书给读者展示一些经典的方法，同时也介绍了作者本人发展的一些方法，并对一些定理给出了数学证明。第二部分则介绍处理实际问题相对复杂且用传统的方法难以分析的技术，主要涉及5种应用，分别为基因组序列数据拷贝数变异探测、信号发生图像的连续监测、输入过程长时间交互缓冲溢出分析、Pickands常数模拟以及基于传感器网络基础的连续改变点检测，而上述应用的例子用经典的方法是难以分析的。

目录

Preface
Acknowledgments
Part I THEORY
1 Introduction
1.1 Distribution of extremes in random fields
1.2 Outline of the method
1.3 Gaussian and asymptotically Gaussian random fields
1.4 Applications
2 Basic examples
2.1 Introduction
2.2 A power-one sequential test
2.3 A kernel-based scanning statistic
2.4 Other methods
3 Approximation of the local rate
3.1 Introduction
3.2 Preliminary localization and approximation
3.2.1 Localization
3.2.2 A discrete approximation
3.3 Measure transformation
3.4 Application of the localization theorem
3.4.1 Checking Condition Ⅰ
3.4.2 Checking Condition Ⅴ
3.4.3 Checking Condition Ⅳ
3.4.4 Checking Condition Ⅱ
3.4.5 Checking Condition Ⅲ
3.5 Integration
4 From the local to the global
4.1 Introduction
4.2 Poisson approximation.of probabilities
4.3 Average run length to false alarm
5 The localization theorem
5.1 Introduction
5.2 A simplified version of the localization theorem
5.3 The localization theorem
5.4 A local limit theorem
5.5 Edge effects and higher order approximations

Part Ⅱ APPLICATIONS
6 Nonparametric tests： Kolmogorov-Smirnov and Peacock
6.1 Introduction
6.1.1 Classical analysis of the Kolmogorov-Smimov test
6.1.2 Peacock's test
6.2 Analysis of the one-dimensional case
6.2.1 Preliminary localization
6.2.2 An approximation by a discrete grid
6.2.3 Measure transformation
6.2.4 The asymptotic distribution of the local field and the global term
6.2.5 Application of the localization theorem and integration
6.2.6 Checking the conditions of the localization theorem
6.3 Peacock's test
6.4 Relations to scanning statistics
……
References
Index

精彩书摘

　　Eachapplication required this modification or that trick in order to apply the basicprinciple. However， after 20 years of repeating the same argument even I wasable to identify the pattern. The thrust of this book is a description of the patternand the demonstration of its usefulness in the analysis of nontrivial statisticalproblems.
　　The basic argument relies on a likelihood ratio identity that uses a sum oflikelihood ratios. This identity translates the original problem that involves theapproximation of a vanishingly small probability to a problem that calls for thesummation of approximations of expectations. The expectations are with respectto alternative distributions in which the event in question is much more likelyto occur. Moreover， by carefully selecting the alternative distributions one mayseparate the leading term in the probability from the expectations that form thesum， enabling the investigation to concentrate on finer effects.
　　The method is useful since it does not rely on the ordering of the parameterset and it does not require the normal distribution. In many applications， someof them are presented in the book， a natural formulation of the model calls forthe use of collections of random variables that are parameterized not by subsetsof the real line. Frequently， the normal assumption may fit the limit in a centrallimit formulation but may not fit as a description of the extreme tall. In all suchcases an alternative to the methods that are usually advocated in the literatureare required. The method we present is such an alternative which we felt othersmay benefit from by knowing about.
　　This is why we wrote the book. But who is the target audience? This is a toughcall. Even if I may state otherwise， the book requires a relatively advanced knowl-edge in probability as background， perhaps at the level of Durrett's book.3 Priorknowledge in statistics is an advantage. Indeed， there is an appendix that liststheorems and results and can be used as reference for the statements that aremade in the book. Still， I guess that this book is not an easy read even forexperts， and much less so for students.
　　With this warning in mind， I hope that the effort that is required in reading thebook will be rewarding. Definitely， for an expert who wants to add yet anothermethod to his toolbox but also for a student who wants to become an expert.For such students， the book can be used as a basis for an advanced seminar.Reading chapters of the book can be used as a primer for a student who is thenrequired to analyze a new problem that was not digested for him/her in the book.This is how I intend to use this book with my students.
　　……
应用统计学丛书·随机域中的极值统计学：理论及应用（英文版） [Extremes in Random Fields A Theory and Its Applications] 下载 mobi epub pdf txt 电子书 格式

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