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From Finite Sample to Asymptotic Methods in Statistics

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ISBN-10: 0521877229

ISBN-13: 9780521877220

Edition: 2nd 2009

Authors: Pranab K. Sen, Julio M. Singer, Antonio C. Pedrosa de Lima

List price: $112.95
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Book details

List price: $112.95
Edition: 2nd
Copyright year: 2009
Publisher: Cambridge University Press
Publication date: 10/30/2009
Binding: Hardcover
Pages: 398
Size: 7.00" wide x 10.00" long x 1.00" tall
Weight: 1.892
Language: English

Julio M. Singer is a Professor at the Department of Statistics, University of S#227;o Paulo, Brazil, and is the co-director of the university's Center for Applied Statistics. Professor Singer is the co-author of books on categorical data and large sample theory and has publications in both methodological and applications-oriented journals. He was the 1993 James E. Grizzle Distinguished Alumnus in Biostatistics from the University of North Carolina at Chapel Hill. He supervised several graduate students and contributed to the development of the doctoral program in statistics at the University of S#227;o Paulo, Brazil.

Antonio C. Pedroso-de-Lima is an Associate Professor at the Department of Statistics, University of Sao Paulo, Brazil, and is the co-director of the university's Center for Applied Statistics. He received his doctoral degree in biostatistics from the University of North Carolina at Chapel Hill. He is the co-author of a book on introductory statistics, and his research has been published in theoretical, methodological, and applications-oriented journals. Professor Pedroso-de-Lima has advised a number of master's degree and doctoral students in the graduate program in statistics at the University of Sao Paulo.

Motivation and Basic Tools
Illustrative Examples and Motivation
Synthesis of Finite to Asymptotic Statistical Methods
The Organization of the Book
Basic Tools and Concepts
Estimation Theory
Basic Concepts
Likelihood, Information, and Sufficiency
Methods of Estimation
Finite Sample Optimality Perspectives
Concluding Notes
Hypothesis Testing
The Neyman-Pearson Paradigm
Composite Hypotheses: Beyond the Neyman-Pearson Paradigm
Invariant Tests
Concluding Notes
Elements of Statistical Decision Theory
Basic Concepts
Bayes Estimation Methods
Bayes Hypothesis Testing
Confidence Sets
Concluding Notes
Stochastic Processes: An Overview
Processes with Markov Dependencies
Discrete Time-Parameter Processes
Continuous Time-Parameter Processes
Stochastic Convergence and Probability Inequalities
Modes of Stochastic Convergence
Probability Inequalities and Laws of Large Numbers
Extensions to Dependent Variables
Miscellaneous Convergence Results
Concluding Notes
Asymptotic Distributions
Some Important Tools
Central Limit Theorems
Rates of Convergence to Normality
Projections and Variance-Stabilizing Transformations
Quadratic Forms
Order Statistics and Empirical Distributions
Concluding Notes
Asymptotic Behavior of Estimators and Tests
Estimating Equations and Local Asymptotic Linearity
Asymptotics for MLE
Asymptotics for Other Classes of Estimators
Asymptotic Efficiency of Estimators
Asymptotic Behavior of Some Test Statistics
Resampling Methods
Concluding Remarks
Categorical Data Models
Nonparametric Goodness-of-Fit Tests
Estimation and Goodness-of-Fit Tests: Parametric Case
Some Other Important Statistics
Concluding Notes
Regression Models
Generalized Least-Squares Procedures
Robust Estimators
Nonlinear Regression Models
Generalized Linear Models
Generalized Least-Squares Versus Generalized Estimating Equations
Nonparametric Regression
Concluding Notes
Weak Convergence and Gaussian Processes
Weak Invariance Principles
Weak Convergence of Partial Sum Processes
Weak Convergence of Empirical Processes
Weak Convergence and Statistical Functionals
Weak Convergence and Nonparametrics
Strong Invariance Principles
Concluding Notes