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

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