Asymptotic Normality of Goodness-Of-Fit Statistics for Sparse Product Multinomials
稀疏乘积多项分布拟合优度统计量的渐近正态性
SUMMARY The asymptotic distribution of the Pearson X 2 and likelihood ratio G 2 goodness-of-fit statistics is derived for k independent, non-identically distributed multinomials, as k approaches infinity, with expected cell frequencies bounded. The application is to large datasets of counts with many zero cells. Conditions are given under which the limiting distributions are normal for originating probabilities (i) known and (ii) dependent on a common, finite-dimensional…