论文标题
零值和替代方面的p值的一般行为
General Behaviour of P-Values Under the Null and Alternative
论文作者
论文摘要
假设检验的结果通常依赖于简单而重要的假设，这些假设是关于零值和替代方案下p值分布的行为的。我们检查了感兴趣的一维参数的测试，该参数会收敛到正态分布，可能是在存在滋扰参数的情况下，并使用来自高级渐近学文献中的技术来表征p值的分布。我们表明，当测试统计量的差异和位置未得到充分校准或测试统计量的高阶累积物不可忽略时，通常持有关于P值分布的信念会产生误导。提出了校正的测试，并显示在某些设置中的表现优于其一阶的测试。
Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to a normal distribution, possibly in the presence of nuisance parameters, and characterize the distribution of the p-values using techniques from the higher order asymptotics literature. We show that commonly held beliefs regarding the distribution of p-values are misleading when the variance and location of the test statistic are not well-calibrated or when the higher order cumulants of the test statistic are not negligible. Corrected tests are proposed and are shown to perform better than their first order counterparts in certain settings.
