Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives
Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440-464) introduced the power divergence statistics, Ra, as multinomial goodness-of-fit statistics. Each Ra has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335-359) derived an asymptotic approximation for the distribution of Ra under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of Ra under nonlocal alternatives can be improved. We apply the expansion to the power approximation for Ra. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test.
Year of publication: |
2004
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Authors: | Sekiya, Yuri ; Taneichi, Nobuhiro |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 91.2004, 2, p. 199-223
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Publisher: |
Elsevier |
Keywords: | Multinomial distribution Goodness-of-fit statistics Power approximation Likelihood ratio test Nonlocal alternative |
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