论文标题
同时拟合优度测试的补充研究
Supplemental Studies for Simultaneous Goodness-of-Fit Testing
论文作者
论文摘要
测试以查看给定数据集是否来自某些指定的分布是统计中最古老的问题之一。已经开发了许多此类测试，并研究了其性能。总体结果是，尽管某个测试可能表现良好，但又名具有良好的力量，在某种情况下，它在其他情况下会严重失败。考虑到分布与零假设中指定的分布有很多不同的方式，这并不奇怪。因此，很难确定要使用的测试的先验。明显的解决方案不是依靠任何一个测试，而是运行其中的几个测试。然而，这导致了同时推断的问题，也就是说，即使进行了多个测试，即使零假设是正确的，也可能只是通过随机偶然地拒绝它。在本文中，我们提出了一种在零假设下产生的P值均匀的方法，无论运行多少个测试。这是通过模拟调整P值来实现的。尽管这种调整方法不是新方法，但以前尚未在拟合优点测试的背景下使用。我们提出了许多模拟研究，这些研究表明P值的均匀性，而其他模拟研究表明，如果在大量情况下平均该测试，则该测试优于任何一个测试。
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied. The general result has been that while a certain test might perform well, aka have good power, in one situation it will fail badly in others. This is not a surprise given the great many ways in which a distribution can differ from the one specified in the null hypothesis. It is therefore very difficult to decide a priori which test to use. The obvious solution is not to rely on any one test but to run several of them. This however leads to the problem of simultaneous inference, that is, if several tests are done even if the null hypothesis were true, one of them is likely to reject it anyway just by random chance. In this paper we present a method that yields a p value that is uniform under the null hypothesis no matter how many tests are run. This is achieved by adjusting the p value via simulation. While this adjustment method is not new, it has not previously been used in the context of goodness-of-fit testing. We present a number of simulation studies that show the uniformity of the p value and others that show that this test is superior to any one test if the power is averaged over a large number of cases.
