# Broken adaptive ridge method for variable selection in generalized partly linear models with application to the coronary artery disease data

## TL;DR

This paper introduces a new statistical method for analyzing high-dimensional data in generalized partly linear models, with an application to coronary artery disease.

## Contribution

The broken adaptive ridge (BAR) estimator is proposed as a novel method for variable selection and parameter estimation in generalized partly linear models.

## Key findings

- The BAR estimator outperforms other penalty-based variable selection methods in simulations.
- The method was applied to coronary artery disease data, revealing new insights in both genetic and non-genetic covariates.

## Abstract

Motivated by the CATHGEN data, we develop a new statistical method for simultaneous variable selection and parameter estimation in the context of generalized partly linear models for data with high-dimensional covariates. The method is referred to as the broken adaptive ridge (BAR) estimator, which is an approximation of the L0-penalized regression by iteratively performing reweighted squared L2-penalized regression. The generalized partly linear model extends the generalized linear model by incorporating a non-parametric component, allowing for the construction of a flexible model to capture various types of covariate effects. We employ the Bernstein polynomials as the sieve space to approximate the non-parametric functions so that our method can be implemented easily using the existing R packages. Extensive simulation studies suggest that the proposed method performs better than other commonly used penalty-based variable selection methods. We apply the method to the CATHGEN data with a binary response from a coronary artery disease study, which motivated our research, and obtained new findings in both high-dimensional genetic and low-dimensional non-genetic covariates.