Slowly Decaying Correlations, Testing Normality, Nuisance Parameters
研究了缓慢衰减的序列相关会导致正态性检验在样本量增大时几乎必然拒绝原假设，发现简单原假设比复合原假设问题更严重，并提出了修正项以改善收敛速度。
Abstract Slowly decaying serial correlations can cause goodness-of-fit tests for a distribution to reject the null hypothesis with probability tending to one with increasing sample size. When the null distribution is completely specified (simple null hypothesis) the problem is actually worse than for the case where there are nuisance parameters to be estimated (composite null hypothesis). In particular, we consider here testing normality. We discuss limit theorems and propose correction terms to be incorporated in certain goodness-of-fit statistics to improve the rates of convergence for the simple hypothesis case. We show how the problem is solved automatically for the composite null hypothesis case when the nuisance parameters are estimated from the data. Simulations illustrate the results.