Work

Nonuniformity of P-values Can Occur Early in Diverging Dimensions

Year: 2017

Type: article

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 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.

Source: PubMed

DOI: 10.48550/arxiv.1705.03604

Authors: Fan, Yingying, Demirkaya, Emre, Lv, Jinchi

Institutions: University of Southern California, University of Tennessee at Knoxville

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Institute of General Medical Sciences

Award: Adaptive Reproducible High-Dimensional Nonlinear Inference for Big Biological Data