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
Summary
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
