Title: Nonuniformity of p-values can occur early in diverging dimensions
Authors: Emre Demirkaya - University of Tennesse, Knoxville (United States) [presenting]
Yingying Fan - University of Southern California (United States)
Jinchi Lv - University of Southern California (United States)
Abstract: 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 powered by classical large-sample asymptotic theory. It is well known that the conventional p-values in the Gaussian linear model are valid even when the dimensionality is a non-vanishing fraction of the sample size. Nevertheless, they 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. Simulation studies confirm the theoretical characterizations.