An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials
研究了当样本量和单元格数都变大时，皮尔逊和似然比统计量的正态近似在中等样本量下的适用性，通过蒙特卡洛方法检验其表现。
Abstract Traditional discussions of goodness-of-fit tests for multinomial data consider asymptotic chi-squared properties under the assumption that all expected cell frequencies become large. This condition is not always satisfied, however, and another asymptotic theory must be considered. For testing a specified simple hypothesis, Morris (1975) and Hoist (1972) gave conditions for the asymptotic normality of the Pearson and likelihood ratio statistics when both the sample size and number of cells become large (even if the expected cell frequencies remain small). Monte Carlo techniques are used to examine the applicability of the normal approximations for moderate sample sizes with moderate numbers of cells.