Abstract
The likelihood ratio chi-square criterion for testing goodness-of-fit in k cell multinomials is known to overestimate significance for small and moderate sample sizes (see, e.g., Larntz (1978)). Therefore, the usual chi-square approximation to the upper tail of the likelihood ratio statistic G 2, is not satisfactory. Several authors have derived adjustments (e.g., Williams (1976), Smith et al. (1981), Hosmane (1987b)), so that the asymptotic mean of G 2 matches the mean of the asymptotic chi-square distribution in the hope that the distribution of G 2 would improve. In this paper, a new adjustment to G 2 is determined on the basis of the n -1-order term (n being the total number) of the Edgeworth expansion of the distribution of smoothed G 2. Monte Carlo results indicate that the modified G 2 outperforms the unadjusted G 2.
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Hosmane, B.S. Smoothing of likelihood ratio statistic for equiprobable multinomial goodness-of-fit. Ann Inst Stat Math 42, 133–147 (1990). https://doi.org/10.1007/BF00050784
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DOI: https://doi.org/10.1007/BF00050784