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错误发现比例的精确计算及其最不利配置应用AI 解读

In a context of multiple hypothesis testing, we provide several new exact calculations related to the false discovery proportion (FDP) of step-up and step-down procedures. For step-up procedures, we show that the number of erroneous rejections conditionally on the rejection number is simply a binomial variable, which leads to explicit computations of the c.d.f., the sth moment and the mean of the FDP, the latter corresponding to the false discovery rate (FDR). For step-down…

高维高斯线性模型的拟合优度检验AI 解读

Let (Y, (Xi)1≤i≤p) be a real zero mean Gaussian vector and V be a subset of {1, …, p}. Suppose we are given n i.i.d. replications of this vector. We propose a new test for testing that Y is independent of (Xi)i∈{1, …, p}∖V conditionally to (Xi)i∈V against the general alternative that it is not. This procedure does not depend on any prior information on the covariance of X or the variance of Y and applies in a high-dimensional setting. It straightforwardly extends to test the…