Introduction to Statistical Limit Theory

Description

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...