High-dimensional regression with a count response

TL;DR

This paper introduces a penalized maximum likelihood estimator for high-dimensional count data regression, demonstrating its theoretical optimality and practical effectiveness through simulations and real data analysis.

Contribution

It proposes a new estimator with adaptive minimaxity for high-dimensional count regression and develops computationally feasible LASSO and SLOPE surrogates.

Findings

Estimator achieves adaptive minimaxity across sparsity levels.

LASSO and SLOPE surrogates perform well in simulations.

Method is effective on real datasets.

Abstract

We consider high-dimensional regression with a count response modeled by Poisson or negative binomial generalized linear model (GLM). We propose a penalized maximum likelihood estimator with a properly chosen complexity penalty and establish its adaptive minimaxity across models of various sparsity. To make the procedure computationally feasible for high-dimensional data we consider its LASSO and SLOPE convex surrogates. Their performance is illustrated through simulated and real-data examples.