High-dimensional regression with a count response

2024/09/13 by Or Zilberman, Felix Abramovich, Zilberman, Or +1
Computer Science · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2409.08821

openalex publication_date 2024/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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