Sen P.K., Singer J.M. Large Sample Methods in Statistics: An Introduction with Applications

Boca Raton: CRC Press, 2017. — 395 p. — ISBN: 978-1-138-10601-7.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.Objectives and Scope: General IntrodutionLarge sample methods: an overview of applications
The organization of this book
Basic tools and concepts
Concluding notes
Exercises
Stochastic ConvergenceModes of stochastic convergence
Probability inequalities and laws of large numbers
Inequalities and laws of large numbers for some dependent variables
Some miscellaneous convergence results
Concluding notes
Exercises
Weak Convergence and Central Limit TheoremsSome im portant tools
Central limit theorems
Projection results and variance-stabilizing transformations
Rates of convergence to normality
Concluding notes
Exercises
Large Sample Behavior of Empirical Distributions and Order StatisticsPreliminary notions
Sample quantiles
Extreme order statistics
Empirical distributions
Functions of order statistics and empirical distributions
Concluding notes
Exercises
Asymptotic Behavior of Estimators and Test StatisticsAsymptotic behavior of maximum likelihood estimators
Asymptotic properties of U-statistics and related estimators
Asymptotic behavior of other classes of estimators
Asymptotic efficiency of estimators
Asymptotic behavior of some test statistics
Concluding notes
Exercises
Large Sample Theory for Categorical Data ModelsNonparametric goodness-of-fit tests
Estimation and goodness-of-fit tests: parametric case
Asymptotic theory for some other im portant statistics
Concluding notes
Exercises
Large Sample Theory for Regression ModelsGeneralized least-squares procedures
Robust estimators
Generalized linear models
Generalized least-squares versus generalized estimating equations
Nonparametric regression
Concluding notes
Exercises
Invariance Principles in Large Sample TheoryWeak invariance principles
Weak convergence of partial sum processes
Weak convergence of empirical processes
Weak convergence and statistical functional
Weak convergence and nonparametrics
Strong invariance principles
Concluding notes
Exercises