A simple procedure based on the average of shifted chi-square statistics (ASCS) is proposed to improve the classical chi-square procedure for testing whether a random sample has been drawn from a specified continuous distribution. We repeatedly partition the sample space, say, ℓ times to obtain ℓ respective chi-square statistics. The proposed test statistic is defined as the average value of the resultant ℓ shifted chi-square statistics. We prove that the ASCS is asymptotically distributed as a weighted sum of a finite number of chi-square variables by the theory of U-statistics. The proposed procedure is shown to be markedly less sensitive to the choice of the anchor position and Monte Carlo experiments demonstrate that it leads to noticeable gains in power.
Journal of Nonparametric Statistics 24(1), pp.39-57