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正依赖对分类数据卡方检验的影响AI 解读

SUMMARY We introduce a general definition of positive dependence for finite-state processes, and show that if successive observations are positively dependent, all tests that are asymptotically equivalent to standard Pearson chi-squared tests have asymptotic null distributions stochastically larger than those obtained under the usual independence assumptions. Ignoring positive dependence therefore leads to too frequent rejection of null hypotheses. This qualitative…

依赖性对卡方与经验分布拟合检验的影响AI 解读

Suppose that a test of fit to a parametric family of distributions is employed, with critical points determined from the limiting null distribution of the test statistic for IID observations. It is shown that if the observations are in fact a stationary process satisfying a positive dependence condition, the test will reject a true null hypothesis too often. This result is established for a broad class of chi squared and empiric df tests, including the Pearson,…

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