On Distributional Properties and Goodness-of-Fit Tests for Generalized Measures of Divergence

摘要

The aim of this work is the investigation of a generalized family of measures of divergence which includes the well-known Csiszdr's, Cressie and Read's, and the Basu-Harris-Hjort-Jones (Basu et ai, 1998) measures. A weakly consistent estimator of the generalized measure of divergence is proposed and its sampling properties and the corresponding asymptotic distribution ane obtained. Finally, tests for multinomial populations are constructed and simulations are performed.