Statistical Inference: The Minimum Distance Approach

Introduction
General Notation
Illustrative Examples
Some Background and Relevant Definitions
Parametric Inference based on the Maximum Likelihood Method
1.Hypothesis Testing by Likelihood Methods
Statistical Functionals and Influence Function
Outline of the Book

Statistical Distances
Introduction
Distances Based on Distribution Functions
Density-Based Distances
Minimum Hellinger Distance Estimation: Discrete Models
Minimum Distance Estimation Based on Disparities: Discrete Models
Some Examples

Continuous Models
Introduction
Minimum Hellinger Distance Estimation
Estimation of Multivariate Location and Covariance
A General Structure
The Basu-Lindsay Approach for Continuous Data
Examples

Measures of Robustness and Computational Issues
The Residual Adjustment Function
The Graphical Interpretation of Robustness
The Generalized Hellinger Distance
Higher Order Influence Analysis
Higher Order Influence Analysis: Continuous Models
Asymptotic Breakdown Properties
The α-Influence Function
Outlier Stability of Minimum Distance Estimators
Contamination Envelopes
The Iteratively Reweighted Least Squares (IRLS)

The Hypothesis Testing Problem
Disparity Difference Test: Hellinger Distance Case
Disparity Difference Tests in Discrete Models
Disparity Difference Tests: The Continuous Case
Power Breakdown of Disparity Difference Tests
Outlier Stability of Hypothesis Tests
The Two Sample Problem

Techniques for Inlier Modification
Minimum Distance Estimation: Inlier Correction in Small Samples
Penalized Distances
Combined Distances
ǫ-Combined Distances
Coupled Distances
The Inlier-Shrunk Distances
Numerical Simulations and Examples

Weighted Likelihood Estimation
The Discrete Case
The Continuous Case
Examples
Hypothesis Testing
Further Reading

Multinomial Goodness-of-fit Testing
Introduction
Asymptotic Distribution of the Goodness-of-Fit Statistics
Exact Power Comparisons in Small Samples
Choosing a Disparity to Minimize the Correction Terms
Small Sample Comparisons of the Test Statistics
Inlier Modified Statistics
An Application: Kappa Statistics

The Density Power Divergence
The Minimum L2 Distance Estimator
The Minimum Density Power Divergence Estimator
A Related Divergence Measure
The Censored Survival Data Problem
The Normal Mixture Model Problem
Selection of Tuning Parameters
Other Applications of the Density Power Divergence

Other Applications
Censored Data
Minimum Hellinger Distance Methods in Mixture Models
Minimum Distance Estimation Based on Grouped Data
Semiparametric Problems
Other Miscellaneous Topics

Distance Measures in Information and Engineering
Introduction
Entropies and Divergences
Csiszar’s f-Divergence
The Bregman Divergence
Extended f-Divergences
Additional Remarks

Applications to Other Models
Introduction
Preliminaries for Other Models
Neural Networks
Fuzzy Theory
Phase Retrieval
Summary