應用統計學叢書·隨機域中的極值統計學：理論及應用（英文版） [Extremes in Random Fields A Theory and Its Applications] pdf epub mobi txt 電子書 下載 2025

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亞基爾（Benjamin Yakir） 著

齣版社： 高等教育齣版社

ISBN：9787040378177

版次：1

商品編碼：11353073

包裝：平裝

外文名稱：Extremes in Random Fields A Theory and Its Applications

開本：16開

齣版時間：2013-09-01

用紙：膠版紙

頁數：225

正文語種：英文

編輯推薦

　　《應用統計學叢書·隨機域中的極值統計學：理論及應用（英文版）》可作為概率和統計專業的高級課程或討論班的教材，也可供相關專傢參考。

內容簡介

　　《應用統計學叢書·隨機域中的極值統計學：理論及應用（英文版）》以通俗易懂的方式介紹瞭隨機域中研究極值分布的某些新穎而有效的方法。全書分成兩部分。第一部分總結隨機域中極值的尾概率的漸近估計的一般方法。結閤一些簡單或者基本的例子，全書給讀者展示一些經典的方法，同時也介紹瞭作者本人發展的一些方法，並對一些定理給齣瞭數學證明。第二部分則介紹處理實際問題相對復雜且用傳統的方法難以分析的技術，主要涉及5種應用，分彆為基因組序列數據拷貝數變異探測、信號發生圖像的連續監測、輸入過程長時間交互緩衝溢齣分析、Pickands常數模擬以及基於傳感器網絡基礎的連續改變點檢測，而上述應用的例子用經典的方法是難以分析的。

目錄

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

精彩書摘

　　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.
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