[原创]Springer ebook8-Nonparametric Monte Carlo Tests and Their Applications

ccpoo

5066

收藏 2007-03-05

Nonparametric Monte Carlo Tests and Their Applications

Series: Lecture Notes in Statistics , Vol. 182
Zhu, Lixing

2005, XII, 184 p., 17 illus., Softcover

ISBN: 978-0-387-25038-0

About this book

A fundamental issue in statistical analysis is testing the fit of a particular probability model to a set of observed data. Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. Nonparametric Monte Carlo Tests and Their Applications proposes a new Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. When there are no nuisance parameters to be estimated, the nonparametric Monte Carlo test can exactly maintain the significance level, and when nuisance parameters exist, this method can allow the test to asymptotically maintain the level.

The author addresses both applied and theoretical aspects of nonparametric Monte Carlo tests. The new methodology has been used for model checking in many fields of statistics, such as multivariate distribution theory, parametric and semiparametric regression models, multivariate regression models, varying-coefficient models with longitudinal data, heteroscedasticity, and homogeneity of covariance matrices. This book will be of interest to both practitioners and researchers investigating goodness-of-fit tests and resampling approximations.

Every chapter of the book includes algorithms, simulations, and theoretical deductions. The prerequisites for a full appreciation of the book are a modest knowledge of mathematical statistics and limit theorems in probability/empirical process theory. The less mathematically sophisticated reader will find Chapters 1, 2 and 6 to be a comprehensible introduction on how and where the new method can apply and the rest of the book to be a valuable reference for Monte Carlo test approximation and goodness-of-fit tests.

Lixing Zhu is Associate Professor of Statistics at the University of Hong Kong. He is a winner of the Humboldt Research Award at Alexander-von Humboldt Foundation of Germany and an elected Fellow of the Institute of Mathematical Statistics.

From the reviews:

"These lecture notes discuss several topics in goodness-of-fit testing, a classical area in statistical analysis. … The mathematical part contains detailed proofs of the theoretical results. Simulation studies illustrate the quality of the Monte Carlo approximation. … this book constitutes a recommendable contribution to an active area of current research." Winfried Stute for Mathematical Reviews, Issue 2006

"...Overall, this is an interesting book, which gives a nice introduction to this new and specific field of resampling methods." Dongsheng Tu for Biometrics, September 2006

Written for:

Researchers and the research students who study statistics and have some knowledge of empirical process theory

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蓝色

2007-3-5 12:30:00

有这么多好书啊，

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蓝色

2007-3-5 12:35:00

有没有 Baltagi, Badi H.的Econometrics 3rd ed.,Springer， 2002
http://www.springer.com/west/home/economics/econometrics?SGWID=4-40534-22-1990154-0

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ccpoo

2007-3-5 13:05:00

以下是引用蓝色在2007-3-5 12:35:00的发言：
有没有 Baltagi, Badi H.的Econometrics 3rd ed.,Springer， 2002
http://www.springer.com/west/home/economics/econometrics?SGWID=4-40534-22-1990154-0

不好意思，我没有这本书的电子版，不过我知道大陆有这本书的影印版出售。

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mark91

2007-7-18 23:25:00

快没钱了啊。

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迎风的石头

2007-11-18 10:02:00

贵呀,楼主能否分享一下?

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stanleyjunjun

2008-5-16 09:22:00

【书名】 Nonparametric Monte Carlo Tests and Their Applications
【作者】 Lixing Zhu
【出版社】Springer
【版本】
【出版日期】2005
【文件格式】PDF
【文件大小】1.39 MB
【页数】168 pages
【ISBN出版号】ISBN-10: 0-387-25038-7;ISBN-13: 978-0387-25038-0
【资料类别】如计量经济学，统计学，笔记，教程，论文等等
【市面定价】59.95 Dollars Amazon Price
【扫描版还是影印版】影印版
【是否缺页】完整
【关键词】Nonparametric, Monte CarloTests
【内容简介】

Monte Carlo approximations to the distributions of statistics have become
important tools in statistics. In statistical inference, Monte Carlo approximation
is performed by comparing the distribution of a statistic based on the
observed data and that based on reference data. How to generate reference
data is a crucial question in this research area.
【目录】

Contents
1 Monte Carlo Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Parametric Monte Carlo Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Nonparametric Monte Carlo Tests (NMCT) . . . . . . . . . . . . . . . . . 2
1.2.1 The Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 NMCT Based on Independent Decompositions . . . . . . . . 4
1.2.3 NMCT Based on Random Weighting . . . . . . . . . . . . . . . . 6
2 Testing for Multivariate Distributions . . . . . . . . . . . . . . . . . . . . . 11
2.1 Four Classes of Multivariate Distributions . . . . . . . . . . . . . . . . . . 11
2.2 A Test Statistic Based on Characteristic Function . . . . . . . . . . . 12
2.3 Simulations and Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.3 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 Asymptotics of Goodness-of-fit Tests for Symmetry . . . . . . . . 27
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.2 Test Statistics and Asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Testing for Elliptical Symmetry . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Testing for Reflection Symmetry . . . . . . . . . . . . . . . . . . . . 30
3.3 NMCT Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3.1 NMCT for Elliptical Symmetry . . . . . . . . . . . . . . . . . . . . . 32
3.3.2 NMCT for Reflection Symmetry. . . . . . . . . . . . . . . . . . . . . 35
3.3.3 A Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 Appendix: Proofs of Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 A Test of Dimension-Reduction Type for Regressions . . . . . 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 The Limit Behavior of Test Statistic . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Monte Carlo Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4.1 Power Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4.2 Residual Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4.3 A Real Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.6 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5 Checking the Adequacy of a Partially Linear Model . . . . . . . 61
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 A Test Statistic and Its Limiting Behavior . . . . . . . . . . . . . . . . . 63
5.2.1 Motivation and Construction . . . . . . . . . . . . . . . . . . . . . . . 63
5.2.2 Estimation of β and γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.3 Asymptotic Properties of the Test . . . . . . . . . . . . . . . . . . . 65
5.3 The NMCT Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.4 Simulation Study and Example . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4.1 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.4.2 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.5.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.5.2 Proof for Results in Section 5.2 . . . . . . . . . . . . . . . . . . . . . 73
5.5.3 Proof for Results in Section 5.3 . . . . . . . . . . . . . . . . . . . . . 82
6 Model Checking for Multivariate Regression Models . . . . . . . 85
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Test Statistics and their Asymptotic Behavior . . . . . . . . . . . . . . . 86
6.2.1 A Score Type Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.2.2 Asymptotics and Power Study . . . . . . . . . . . . . . . . . . . . . . 87
6.2.3 The Selection of W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.4 Likelihood Ratio Test for Regression Parameters . . . . . . 90
6.3 NMCT Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.3.1 The NMCT for TTn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.3.2 The NMCT for the Wilks Lambda . . . . . . . . . . . . . . . . . . . 93
6.4 Simulations and Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.4.1 Model Checking with the Score Type Test . . . . . . . . . . . . 94
6.4.2 Diagnostics with the Wilks Lambda . . . . . . . . . . . . . . . . . 96
6.4.3 An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7 Heteroscedasticity Tests for Regressions . . . . . . . . . . . . . . . . . . . 103
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.2 Construction and Properties of Tests . . . . . . . . . . . . . . . . . . . . . . 104
7.2.1 Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.2.2 The Limit Behavior of Tn and Wn . . . . . . . . . . . . . . . . . . 105
7.3 Monte Carlo Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.4 A Simulation Study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.5 Proofs of the theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.5.1 A Set of Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.5.2 Proofs of the Theorems in Section 2 . . . . . . . . . . . . . . . . . 115
7.5.3 Proofs of the Theorems in Section 3 . . . . . . . . . . . . . . . . . 120
8 Checking the Adequacy of a Varying-Coefficients Model . . 123
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
8.2 Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.3 The Limit Behavior of Test Statistic . . . . . . . . . . . . . . . . . . . . . . 126
8.3.1 Innovation Process Approach . . . . . . . . . . . . . . . . . . . . . . . 128
8.3.2 A Non-parametric Monte Carlo Test . . . . . . . . . . . . . . . . . 130
8.4 Simulation Study and Application . . . . . . . . . . . . . . . . . . . . . . . . 131
8.4.1 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
8.4.2 Application to AIDS Data . . . . . . . . . . . . . . . . . . . . . . . . . . 133
8.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9 On the Mean Residual Life Regression Model . . . . . . . . . . . . . 141
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
9.2 Asymptotic Properties of the Test Statistic. . . . . . . . . . . . . . . . . 142
9.3 Monte Carlo Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
9.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
9.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
10 Homegeneity Testing for Covariance Matrices . . . . . . . . . . . . . 155
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
10.2 Construction of Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
10.3 Monte Carlo Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.3.1 Classical Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
10.3.2 NMCT Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
10.3.3 Permutation Test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
10.3.4 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
10.4 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
【书评好书

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limit912

2008-5-17 14:21:00

楼主果然是牛人,谢谢分享了.

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jacques97

2008-5-17 15:15:00

http://rapidshare.de/files/29930216/029_002.pdf
这也可以下载,就是太慢了,呵呵:)另外7楼也介绍的很详细了:)

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jacques97

2008-5-17 15:19:00

我有这本书:)给你个地址你自己下吧.http://mihd.net/h8jpse

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myxixi

2008-5-17 21:20:00

楼主绝对是牛人！

谢谢

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Nonparametric Monte Carlo Tests and Their Applications

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