《隨機域中的極值統計學:理論及套用(英文版)》以通俗易懂的方式介紹了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機率的漸近估計的一般方法。結合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，同時也介紹了作者本人發展的一些方法，並對一些定理給出了數學證明。第二部分則介紹處理實際問題相對複雜且用傳統的方法難以分析的技術，主要涉及5種套用，分別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、輸入過程長時間互動緩衝溢出分析、Pickands常數模擬以及基於感測器網路基礎的連續改變點檢測，而上述套用的例子用經典的方法是難以分析的。
基本介紹
- 書名：隨機域中的極值統計學:理論及套用
- 作者：亞基爾 (Benjamin Yakir)
- 出版日期：2013年9月1日
- 語種：英語
- ISBN：7040378175
- 外文名：Extremes in Random Fields A Theory and Its Applications
- 出版社：高等教育出版社
- 頁數：225頁
- 開本：16
- 品牌：高教社
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《隨機域中的極值統計學:理論及套用(英文版)》可作為機率和統計專業的高級課程或討論班的教材，也可供相關專家參考。
作者簡介
作者：（以色列）亞基爾（Benjamin Yakir）
圖書目錄
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
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
