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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,…

观测依赖对卡方拟合检验的影响AI 解读

Tests of fit that assume i.i.d. observations may be affected by dependence among the observations. This effect is studied for the Pearson chi squared test when the data form a stationary stochastic process. The general form of asymptotic distribution theory under the null hypothesis is outlined and examples are given. For testing fit to a specified normal law, it is shown that when observations come from a quite general class of Gaussian stationary processes, positive…