Statistical Inference Based on Divergence Measures (Hardcover)

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