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多项分布拟合优度检验的功效近似AI 解读

Multinomial tests for the fit of iid observations X 1 …, Xn to a specified distribution F are based on the counts Ni of observations falling in k cells E 1, …, Ek that partition the range of the X j . The earliest such test is based on the Pearson (1900) chi-squared statistic: X 2 = Σ k i=1 (Ni – npi )2/npi , where pi = PF (Xj in Ei ) are the cell probabilities under the null hypothesis. A common competing test is the likelihood ratio test based on LR = 2 Σ k i=1 Ni…

卡方拟合优度检验中的分组数选择AI 解读

The power of Pearson chi-squared and likelihood ratio goodness-of-fit tests based on different partitions is studied by considering families of densities “between” the null density and fixed alternative densities. For sample sizes n → ∞, local asymptotic theory with respect to the number of classes k is developed for such families. Simple sufficient and almost necessary conditions are derived under which it is asymptotically optimal to let k tend to infinity with n. A…