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We consider goodness-of-fit tests for uniformity of a multinomialdistribution 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 anasymptotic regime, where the number of cells grows with the sample size. Mostattention is focused on the class of power divergence statistics. The aim ofthis article is to study the intermediate asymptotic relative efficiency of twotests, where the powers of the tests are asymptotically non-degenerate and thesequences of alternatives converge to the hypothesis, but not too fast. Theintermediate asymptotic relative efficiency of the chi-square test wrt anarbitrary symmetric test is considered in details.

On the intermediate asymptotic efficiency of goodness-of-fit tests in multinomial distributions