Preface
Notation
1. Introduction
1.1. Approximate Statistical Procedures
1.2. Asymptotic Optimality Theory
1.3. Limitations
1.4. The Index n
2. Stochastic Convergence
2.1. Basic Theory
2.2. Stochastic o and O Symbols
2.3. Characteristic Functions
2.4. Almost-Sure Representations
2.5. Convergence of Moments
2.6. Convergence-Determining Classes
2.7. Law of the Iterated Logarithm
2.8. Lindeberg-Feller Theorem
2.9. Convergence in Total Variation
Problems
3. Delta Method
3.1. Basic Result
3.2. Variance-Stabilizing Transformations
3.3. Higher-Order Expansions
3.4. Uniform Delta Method
3.5. Moments
Problems
4. Moment Estimators
4.1. Method of Moments
4.2. Exponential Families
Problems
5. M- and Z-Estimators
5.1. Introduction
5.2. Consistency
5.3. Asymptotic Normality
5.4. Estimated Parameters
5.5. Maximum Likelihood Estimators
5.6. Classical Conditions
5.7. One-Step Estimators
5.8. Rates of Convergence
5.9. Argmax Theorem
Problems
6. Contiguity
6.1. Likelihood Ratios
6.2. Contiguity
Problems
7. Local Asymptotic Normality
7.1. Introduction
7.2. Expanding the Likelihood
7.3. Convergence to a Normal Experiment
7.4. Maximum Likelihood
7.5. Limit Distributions under Alternatives