标题： p值的非均匀性可以在发散维度早期出现 显示英文标题

标题： Nonuniformity of P-values Can Occur Early in Diverging Dimensions

摘要： 评估协变量的联合显著性在广泛的应用中具有根本的重要性。 为此，通常使用由经典的大样本渐近理论驱动的算法所生成的p值。 众所周知，在高斯线性模型中，传统的p值即使当维数是样本量的非消失分数时仍然有效，但在设计矩阵在更高维度下变得奇异或误差分布偏离高斯性时可能会失效。 一个自然的问题是在广义线性模型中，传统的p值在发散维度下何时会失效。 我们证明了在非线性模型中这种失效可以很早就发生。 我们的理论特征通过模拟研究得到了验证。 显示英文摘要

摘要： Evaluating the joint significance of covariates is of fundamental importance in a wide range of applications. To this end, p-values are frequently employed and produced by algorithms that are powered by classical large-sample asymptotic theory. It is well known that the conventional p-values in Gaussian linear model are valid even when the dimensionality is a non-vanishing fraction of the sample size, but can break down when the design matrix becomes singular in higher dimensions or when the error distribution deviates from Gaussianity. A natural question is when the conventional p-values in generalized linear models become invalid in diverging dimensions. We establish that such a breakdown can occur early in nonlinear models. Our theoretical characterizations are confirmed by simulation studies.