On the intermediate asymptotic efficiency of goodness-of-fit tests in multinomial distributions
ESAIM: Probability and Statistics, Tome 26 (2022), pp. 473-494

We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime, where the number of cells grows with the sample size. Most attention is focused on the class of power divergence statistics. The aim of this article is to study the intermediate asymptotic relative efficiency of two tests, where the powers of the tests are asymptotically non-degenerate and the sequences of alternatives converge to the hypothesis, but not too fast. The intermediate asymptotic relative efficiency of the χ2 test wrt an arbitrary symmetric test is considered in details.

DOI : 10.1051/ps/2022010
Classification : 62G10, 62G20
Keywords: Asymptotic efficiency, χ2 statistic, log-likelihood ratio statistic, goodness-of-fit tests, multinomial distribution, power divergence statistics 
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     title = {On the intermediate asymptotic efficiency of goodness-of-fit tests in multinomial distributions},
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Mirakhmedov, Sherzod M. On the intermediate asymptotic efficiency of goodness-of-fit tests in multinomial distributions. ESAIM: Probability and Statistics, Tome 26 (2022), pp. 473-494. doi: 10.1051/ps/2022010

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