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

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  • Wegenkittl, Stefan

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.

Suggested Citation

  • Wegenkittl, Stefan, 2002. "A Generalized [phi]-Divergence for Asymptotically Multivariate Normal Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 288-302, November.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:288-302
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    References listed on IDEAS

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    1. Menendez, M. & Morales, D. & Pardo, L. & Vajda, I., 1995. "Divergence-Based Estimation and Testing of Statistical Models of Classification," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 329-354, August.
    2. Salicru, M. & Morales, D. & Menendez, M. L. & Pardo, L., 1994. "On the Applications of Divergence Type Measures in Testing Statistical Hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 372-391, November.
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