Statistical Inference Based on Divergence Measures

by Pardo, Leandro

• ISBN13: 9781420034813
• ISBN10: 1420034812
• Copyright: 2005-10-10
• Publisher: Taylor & Francis

Summary

Organized in systematic way, Statistical Inference Based on Divergence Measures presents classical problems of statistical inference, such as estimation and hypothesis testing, on the basis of measures of entropy and divergence with applications to multinomial and generation populations. On the basis of divergence measures, this book introduces minimum divergence estimators as well as divergence test statistics and compares them to the classical maximum likelihood estimator, chi-square test statistics, and the likelihood ratio test in different statistical problems. The text includes over 120 exercises with solutions, making it ideal for students with a basic knowledge of statistical methods.

Table of Contents

Divergence Measures: Definition And Properties

Introduction

Phi-divergence. Measures between Two Probability Distributions: Definition and Properties

Other Divergence Measures between Two Probability Distributions

Divergence among k Populations

Phi-disparities

Exercises

Answers to Exercises

Entropy As A Measure Of Diversity: Sampling Distributions

Introduction

Phi-entropies. Asymptotic Distribution

Testing and Confidence Intervals for Phi-entropies

Multinomial Populations: Asymptotic Distributions

Maximum Entropy Principle and Statistical Inference on Condensed Ordered Data

Exercises

Answers to Exercises

Goodness-Of-Fit: Simple Null Hypothesis

Introduction

Phi-divergences and Goodness-of-fit with Fixed Number of Classes

Phi-divergence Test Statistics under Sparseness Assumptions

Nonstandard Problems: Tests Statistics based on Phi-divergences

Exercises

Answers to Exercises

Optimality Of Phi-Divergence Test Statistics In Goodness-Of-Fit

Introduction

Asymptotic Effciency

Exact and Asymptotic Moments: Comparison

A Second Order Approximation to the Exact Distribution

Exact Powers Based on Exact Critical Regions

Small Sample Comparisons for the Phi-divergence Test Statistics

Exercises

Answers to Exercises

Minimum Phi-Divergence Estimators

Introduction

Maximum Likelihood and Minimum Phi-divergence Estimators

Properties of the Minimum Phi-divergence Estimator

Normal Mixtures: Minimum Phi-divergence Estimator

Minimum Phi-divergence Estimator with Constraints: Properties

Exercises

Answers to Exercises

Goodness-Of-Fit: Composite Null Hypothesis

Introduction

Asymptotic Distribution with Fixed Number of Classes

Nonstandard Problems: Test Statistics Based on Phi-divergences

Exercises

Answers to Exercises

Testing Loglinear Models Using Phi-divergence Test Statistics

Introduction

Loglinear Models: Definition

Asymptotic Results for Minimum Phi-divergence Estimators in Loglinear Models

Testing in Loglinear Models

Simulation Study

Exercises

Answers to Exercises

Phi-Divergence Measures In Contingency Tables

Introduction

Independence

Symmetry

Marginal Homogeneity

Quasi-symmetry

Homogeneity

Exercises

Answers to Exercises

Testing In General Populations

Introduction

Simple Null Hypotheses: Wald, Rao, Wilks and Phi-divergence Test Statistics

Composite Null Hypothesis

Multi-sample Problem

Some Topics in Multivariate Analysis

Exercises

Answers to Exercises

References

Index

Table of Contents provided by Publisher. All Rights Reserved.