Statistical Inference Based on Divergence Measures

ISBN: 9781584886006 出版年：2018 页码：513 Pardo, Leandro CRC Press

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