Effect of Some Estimators on a Large Sample Approximation to the Non-Null Distribution of the Pearson Chi-Square Statistic.

In this paper three distinct formulations of the Pearson chi-square test statistic, each of which employs random interval boundaries, are considered in presenting an answer to the following problem: Given a finite sample size and specified fixed composite null and alternative hypotheses, which method of estimation of the unknown parameters leads to a test which is most sensitive to departures from the null hypothesis in the direction of the fixed alternative? The proposed answer is based on a finite sample size approximation to the distribution of the appropriate quadratic form under the alternative hypothesis. Key words: Pearson chi-square test, Test of fit, Asymptotic distribution.