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E-book
Author Polansky, Alan M.

Title Introduction to statistical limit theory / Alan M. Polansky
Published Boca Raton, FL : Chapman & Hall/CRC Press, [2011]
©2011
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Description 1 online resource (xx, 625 pages) : illustrations
Series Chapman & Hall/CRC texts in statistical science series
Texts in statistical science.
Contents ; Differentiation of Statistical Functionals; Expansion Theory for Statistical Functionals; Asymptotic Distribution Parametric Inference; Introduction; Point Estimation; Confidence Intervals; Statistical Hypothesis Tests; Observed Confidence Levels; Bayesian Estimation Nonparametric Inference; Introduction; Unbiased Estimation and U -Statistics; Linear Rank Statistics; Pitman Asymptotic Relative Efficiency; Density Estimation; The Bootstrap Appendix A: Useful Theorems and Notation; Appendix B: Using R for Experimentation References Exercises and Experiments appear at the end of each chapter
Normal Approximation; The Sample Moments; The Sample Quantiles Convergence of Moments; Convergence in rth Mean; Uniform Integrability; Convergence of Moments Central Limit Theorems; Introduction; Non-Identically Distributed Random Variables; Triangular Arrays; Transformed Random Variables Asymptotic Expansions for Distributions; Approximating a Distribution; Edgeworth Expansions; The Cornish-Fisher Expansion; The Smooth Function Model; General Edgeworth and Cornish-Fisher Expansions; Studentized Statistics; Saddlepoint Expansions Asymptotic Expansions for Random Variables; Approximating Random Variables; Stochastic Order Notation; The Delta Method; The Sample Moments Differentiable Statistical Functionals; Introduction; Functional Parameters and Statistics
Sequences of Real Numbers and Functions; Introduction; Sequences of Real Numbers; Sequences of Real Functions; The Taylor Expansion; Asymptotic Expansions; Inversion of Asymptotic Expansions Random Variables and Characteristic Functions; Introduction; Probability Measures and Random Variables; Some Important Inequalities; Some Limit Theory for Events; Generating and Characteristic Functions Convergence of Random Variables; Introduction; Convergence in Probability; Stronger Modes of Convergence; Convergence of Random Vectors; Continuous Mapping Theorems; Laws of Large Numbers; The Glivenko-Cantelli Theorem; Sample Moments; Sample Quantiles Convergence of Distributions; Introduction; Weak Convergence of Random Variables; Weak Convergence of Random Vectors; The Central Limit Theorem; The Accuracy of the
Summary "Helping students develop a good understanding of asymptotic theory, Introduction to Statistical Limit Theory provides a thorough yet accessible treatment of common modes of convergence and their related tools used in statistics. It also discusses how the results can be applied to several common areas in the field. The author explains as much of the background material as possible and offers a comprehensive account of the modes of convergence of random variables, distributions, and moments, establishing a firm foundation for the applications that appear later in the book. The text includes detailed proofs that follow a logical progression of the central inferences of each result. It also presents in-depth explanations of the results and identifies important tools and techniques. Through numerous illustrative examples, the book shows how asymptotic theory offers deep insight into statistical problems, such as confidence intervals, hypothesis tests, and estimation. With an array of exercises and experiments in each chapter, this classroom-tested book gives students the mathematical foundation needed to understand asymptotic theory. It covers the necessary introductory material as well as modern statistical applications, exploring how the underlying mathematical and statistical theories work together"--Provided by publisher
"Those moving on to advanced statistics typically lack the mathematical foundation that allows them to make full use of statistical limit theory. This accessible resource reviews approximation theory and limit theory for sequences of functions and basic notions of functional analysis. It provides detailed arguments that show how underlying mathematical and statistical theory work together. Among its unique qualities, the text covers expansion theory, which is becoming increasingly important in modern applications. It also discusses bootstrap, kernel smoothing, and Markov chain Monte Carlo and includes a wide array of examples and problems from the fundamental to very advanced"--Provided by publisher
Bibliography Includes bibliographical references and index
Subject Limit theorems (Probability theory)
Limit theorems (Probability theory)
MATHEMATICS / Applied
MATHEMATICS / Probability & Statistics / General
Form Electronic book
ISBN 1420076612
9781420076615