The CDF penalty:sparse and quasi unbiased estimation in regression models

TL;DR

This paper introduces a new penalty for high-dimensional regression that ensures sparse variable selection, quasi-unbiasedness, and solution uniqueness, improving model interpretability and estimation accuracy.

Contribution

The paper proposes a novel penalty method that guarantees sparsity, quasi-unbiasedness, and uniqueness in high-dimensional regression models, addressing key challenges in variable selection.

Findings

Performs comparably to existing methods in simulations

Ensures unique solutions in high-dimensional settings

Guarantees sparse and quasi-unbiased coefficient estimates

Abstract

In high-dimensional regression modelling, the number of candidate covariates to be included in the predictor is quite large, and variable selection is crucial. In this work, we propose a new penalty able to guarantee both sparse variable selection, i.e. exactly zero regression coefficient estimates, and quasi-unbiasedness for the coefficients of 'selected' variables in high dimensional regression models. Simulation results suggest that our proposal performs no worse than its competitors while always ensuring that the solution is unique.