随机域中的极值统计学(英文版)(Extremes In Random Fields: A Theory and its Applications)

定　　价：59 元

• 作者：亚基尔 (Benjamin Yakir) 　著
• 出版时间：2013/9/1
• ISBN：9787040378177
• 出 版 社：高等教育出版社

• 中图法分类：C8 
• 页码：225
• 纸张：胶版纸
• 版次：1
• 开本：16开

内容简介

　　《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
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
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

Preface
Acknowledgments
Part I THEORY
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
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
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
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