Minimax Optimal Estimator and Improved Error Rate for the MLE in Logistic Regression with Gaussian Design

Junren Chen, Arya Mazumdar

We study finite-sample parameter estimation in logistic regression with Gaussian design, where the goal is to estimate ${\theta }^{\ast }\in {\mathbb{R}}^d$ with $R=\Vert {\theta }^{\ast }{\Vert }_2\ge 1$ f…