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arge Sample Methods in Statistics: An Introduction with Applications (Chapman & Hall/CRC Texts in Statistical Science) [color=rgb(136, 136, 136) !important]Hardcover [color=rgb(136, 136, 136) !important]– January 1, 1993
by Pranab K. Sen (Author), Julio M. Singer (Author)
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[color=rgb(136, 136, 136) !important]ISBN-13: 978-0412042218 [color=rgb(136, 136, 136) !important]ISBN-10: 0412042215 [color=rgb(136, 136, 136) !important]Edition: Softcover reprint of the original 1st ed. 1993
This text bridges the gap between sound theoretcial developments and practical, fruitful methodology by providing solid justification for standard symptotic statistical methods. It contains a unified survey of standard large sample theory and provides access to more complex statistical models that arise in diverse practical applications.
A VERY CLASSICAL BOOK IN STATISTICS.
Contents
Preface
1 Objectives and Scope: General Introduction
1.1 Introduction
1.2 Large sample methods: an overview of applications
1.3 The organization of this book
1.4 Basic tools and concepts
1.5 Concluding notes
1.6 Exercises
2 Stochastic Convergence
2.1 Introduction
2.2 Modes of stochastic convergence 34
2.3 Probability inequalities and laws of large numbers 48
2.4 Inequalities and laws of large numbers for some dependent
variables 72
2.5 Some miscellaneous convergence results 85
2.6 Concluding notes 91
2.7 Exercises 92
3 Weak Convergence and Central Limit Theorems
3.1 Introduction
3.2 Some important tools 102
3.3 Central limit theorems 107
3.4 Projection results and variance-stabilizing transformations 125
3.5 Rates of convergence to normality 147
3.6 Concluding notes 151
3.7 Exercises 152
4 Large Sample Behavior of Empirical Distributions and Order
Statistics 155
4.1 Introduction 155
4.2 Preliminary notions 157
4.3 Sample quantiles 166
4.4 Extreme order statistics 173
4.5 Empirical distributions 184
4.6 Functions of order statistics and empirical distributions 188
4.7 Concluding notes 195
4.8 Exercises 195
5 Asymptotic Behavior of Estimators and Test Statistics 201
5.1 Introduction 201
5.2 Asymptotic behavior of maximum likelihood estimators 202
5.3 Asymptotic properties of U-statistics and related estimators 210
5.4 Asymptotic behavior of other classes of estimators
5.5 Asymptotic efficiency of estimators
5.6 Asymptotic behavior of some test statistics
5.7 Concluding notes
5.8 Exercises
6 Large Sample Theory for Categorical Data Models 247
6.1 Introduction 247
6.2 Nonparametric goodness-of-fit tests 249
6.3 Estimation and goodness-of-fit tests: parametric case 253
6.4 Asymptotic theory for some other important statistics 262
6.5 Concluding notes 266
6.6 Exercises 266
7 Large Sample Theory for Regression Models 273
7.1 Introduction 273
7.2 Generalized least-squares procedures 276
7.3 Robust estimators 291
7.4 Generalized linear models 300
7.5 Generalized least-squares versus generalized estimating
equations 314
7.6 N onparametric regression
7.7 Concluding notes
7.8 Exercises
Invariance Principles in Large Sample Theory
8.1 Introduction
8.2 Weak invariance principles
8.3 Weak convergence of partial sum processes
8.4 Weak convergence of empirical processes
8.5 Weak convergence and statistical functionals
8.6 Weak convergence and nonparametrics
8.7 Strong invariance principles
8.8 Concluding notes
8.9 Exercises
References
Index
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