Asymptotic laws for stochastic disparity statistics. (English) Zbl 1154.62334

Summary: This paper simplifies and clarifies the conditions of the famous theorem of Morris dealing with the asymptotic distribution of the Pearson goodness- of-fit statistic when the number of partition cells depends on sample size. The local character of alternatives implicitly required by the mentioned theorem is expressed explicitly, in terms of a Pearson distance between the hypothesis and alternative. Moreover, the paper extends the theorem of Morris to a wide class of disparity statistics by proving that appropriately standardized versions of these statistics and the Pearson statistic are asymptotically equivalent. The paper is restricted to the important particular case where the partition cells are equiprobable under the hypothesis.


62G20 Asymptotic properties of nonparametric inference
62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics