Introduction to Statistical Limit Theory

✍ Scribed by Polansky, Alan M

• Publisher: CRC Press
• Year: 2011
• Tongue: English
• Leaves: 633
• Series: Chapman & Hall/CRC Texts in Statistical Science
• Category: Library

✦ Synopsis

Sequences of Real Numbers and Functions Introduction Sequences of Real Numbers Sequences of Real Functions The Taylor Expansion Asymptotic Expansions Inversion of Asymptotic ExpansionsRandom Variables and Characteristic Functions Introduction Probability Measures and Random VariablesSome Important Inequalities Some Limit Theory for EventsGenerating and Characteristic FunctionsConvergence of Random Variables Introduction Convergence in ProbabilityStronger Modes of ConvergenceConvergence of Random Vectors Continuous Mapping Theorems Laws of Large Numbers The Glivenko-Cantelli TheoremSample Momen. Read more...

Abstract:

Reviews approximation theory and limit theory for sequences of functions and basic notions of functional analysis. This title provides arguments that show how underlying mathematical and statistical theory work together. It covers expansion theory and discusses bootstrap, kernel smoothing, and Markov chain Monte Carlo. Read more...

✦ Table of Contents

Content: Cover
Title
Copyright
Contents
Preface
CHAPTER 1: Sequences of Real Numbers and Functions
CHAPTER 2: Random Variables and Characteristic Functions
CHAPTER 3: Convergence of Random Variables
CHAPTER 4: Convergence of Distributions
CHAPTER 5: Convergence of Moments
CHAPTER 6: Central Limit Theorems
CHAPTER 7: Asymptotic Expansions for Distributions
CHAPTER 8: Asymptotic Expansions for Random Variables
CHAPTER 9: Differentiable Statistical Functionals
CHAPTER 10: Parametric Inference
CHAPTER 11: Nonparametric Inference
APPENDIX A: Useful Theorems and Notation

✦ Subjects

Limit theorems (Probability theory).