Improvements of goodness-of-fit statistics for sparse multinomials based on normalizing transformations
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We consider multinomial goodness-of-fit tests for a specified simple hypothesis under the assumption of sparseness. It is shown that the asymptotic normality of the PearsonX 2 statistic (X k 2 ) and the log-likelihood ratio statistic (G k 2 ) assuming sparseness. In this paper, we improve the asymptotic normality ofX k 2 andG k 2 statistics based on two kinds of normalizing transformation. The performance of the transformed statistics is numerically investigated.
Key words and phrasesNormalizing transformation PearsonX2 statistic log-likelihood ratio statistic sparse multinomials
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