**Introduction**

General Notation

Illustrative Examples

Some Background and Relevant Definitions

Parametric Inference based on the Maximum Likelihood Method

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