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类别数趋于无穷时位置—尺度模型的广义卡方拟合优度检验AI 解读

In this paper we consider generalized chi-square goodness-of-fit tests based on increasingly finer partitions (as the sample size increases) for models with location-scale nuisance parameters. The asymptotic distributions are derived both under the null hypothesis and under local alternatives, obtained by taking contamination families of densities between the null hypothesis and fixed alternative hypotheses. If the number of random cells increases to infinity, the…

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…