A generalized φ-divergence for asymptotically multivariate normal models

[摘要] Csiszar's (Magyar. Tud. Akad. Mat. Kutato Int. Kozl 8 (1963), 85-108) phi-divergence, which was considered independently by M. S. Ali and S. D. Silvey (J. R. Statist. Soc. Ser. B 28 (1966), 131-142) gives a goodness-of-fit statistic for multinomial distributed data. We define a generalized phi-divergence that unifies the phi-divergence approach with that of C. R. Rao and S. K. Mitra (Generalized Inverse of Matrices and Its Applications, Wiley, New York, 1971) and derive weak convergence to a chi(2) distribution under the assumption of asymptotically multivariate normal distributed data vectors. As an example we discuss the application to the frequency count in Markov chains and thereby give a goodness-of-fit test for observations from dependent processes with finite memory. (C) 2002 Elsevier Science (USA).

[发布日期] 2002-11-01

[关键词] distribution of statistics;hypothesis testing;Markov processes;hypothesis testing (Inference from stochastic processes);asymptotic distribution theory