**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 Normal Approximation

The Sample Moments

The Sample Quantiles

**Convergence of Moments **

Convergence in r^{th} 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

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**