A note on "MLE in logistic regression with a diverging dimension"

TL;DR

This paper highlights an error in the proof of high-dimensional asymptotic normality of the MLE in logistic regression when the number of covariates diverges with sample size.

Contribution

It identifies a flaw in the existing proof of asymptotic normality for MLE in high-dimensional logistic regression models.

Findings

The proof in the referenced paper is incorrect.

The asymptotic normality result needs revision.

Implications for high-dimensional logistic regression analysis.

Abstract

This short note is to point the reader to notice that the proof of high dimensional asymptotic normality of MLE estimator for logistic regression under the regime $p_n=o(n)$ given in paper: "Maximum likelihood estimation in logistic regression models with a diverging number of covariates. Electronic Journal of Statistics, 6, 1838-1846." is wrong.