A Generalized [phi]-Divergence for Asymptotically Multivariate Normal Models

Stefan Wegenkittl

Journal of Multivariate Analysis, 2002, vol. 83, issue 2, 288-302

Abstract: I. Csiszár's (Magyar. Tud. Akad. Mat. Kutató Int. Közl8 (1963), 85-108) [phi]-divergence, which was considered independently by M. S. Ali and S. D. Silvey (J. R. Statist. Soc. Ser. B28 (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.

Keywords: distribution; of; statistics; hypothesis; testing; Markov; processes:; hypothesis; testing; (Inference; from; stochastic; processes); asymptotic; distribution; theory (search for similar items in EconPapers)
Date: 2002
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