# Nonuniformity of P-values Can Occur Early in Diverging Dimensions

arXiv: https://arxiv.org/abs/1705.03604 · HTML: https://mlsanity.com/paper/1705.03604/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2017.

## Built on by (most cited first, 3 of 3)

- [SLOE: A Faster Method for Statistical Inference in High-Dimensional Logistic Regression](https://mlsanity.com/paper/2103.12725/) (2021)
- [Error-based Knockoffs Inference for Controlled Feature Selection](https://mlsanity.com/paper/2203.04483/) (2022)
- [Confidence Sets under Generalized Self-Concordance](https://mlsanity.com/paper/2301.00260/) (2022)

## Abstract (arXiv)

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.