Asymptotically Optimal Tests for Multinomial Distributions

摘要: Tests of simple and composite hypotheses for multinomial distributions are considered. It is assumed that the size αN a test tends to 0 as sample N increases. The main concern this paper substantiate following proposition: If given “sufficiently different” from likelihood ratio then there ≦αN which considerably more powerful than at “most” points in set alternatives when large enough, provided → suitable rate. In particular, it shown chi-square tests some inferior, sense described, corresponding tests. Certain Bayes share above-mentioned property test.