非参数方法控制虚假发现比例的中位数
Nonparametric methods controlling the median of the false discovery proportion
AI总结：
本文提出了一种非参数多重检验方法，用于控制虚假发现比例的中位数，适用于多种参数假设检验场景。
摘要：
在检验许多假设时，我们通常没有关于效应方向的强烈预期。然而在某些情况下，备择假设是参数位于某个方向或区间内，并且实际上预期大多数假设是假的。这经常发生在研究人员进行多重非劣性或等价性检验时，例如在用代谢物数据测试食品安全时。目标是利用数据来证实大多数假设是假的的预期。我们提出了一种非参数多重检验方法，这种在这种情况下的方法具有强大性。如果用户的预期错误，我们的方法仍然有效但功率低。当然，当适当使用单侧而不是双侧检验时，所有多重检验方法都会更强大，但我们的方法通常具有更高的功率。本文提出的方法并不局限于安全测试，可以用于测试各种参数的假设，如模型的系数。本文的方法控制了虚假发现比例（FDP）的中位数，即被拒绝假设中虚假发现的比例。这种方法与控制虚假发现率（FDR）类似，其中确保的是FDP的均值而不是中位数较小。我们的程序利用了检验统计量的对称性质，不需要独立性，并具有有限样本性质。
英文摘要：
When testing many hypotheses, often we do not have strong expectations about the directions of the effects. In some situations however, the alternative hypotheses are that the parameters lie in a certain direction or interval, and it is in fact expected that most hypotheses are false. This is often the case when researchers perform multiple noninferiority or equivalence tests, e.g. when testing food safety with metabolite data. The goal is then to use data to corroborate the expectation that most hypotheses are false. We propose a nonparametric multiple testing approach that is powerful in such situations. If the user's expectations are wrong, our approach will still be valid but have low power. Of course all multiple testing methods become more powerful when appropriate one-sided instead of two-sided tests are used, but our approach often has superior power then. The proposed methods are not at all limited to safety testing and can be used for testing hypotheses about various kinds of parameters, such as coefficients of a model. The methods in this paper control the median of the false discovery proportion (FDP), which is the fraction of false discoveries among the rejected hypotheses. This approach is comparable to false discovery rate control, where one ensures that the mean rather than the median of the FDP is small. Our procedures make use of a symmetry property of the test statistics, do not require independence and have finite-sample properties.
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