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Motivated by the CATHGEN data, we develop a new statistical learning methodfor simultaneous variable selection and parameter estimation under the contextof generalized partly linear models for data with high-dimensional covariates.The method is referred to as the broken adaptive ridge (BAR) estimator, whichis an approximation of the $L_0$-penalized regression by iteratively performingreweighted squared $L_2$-penalized regression. The generalized partly linearmodel extends the generalized linear model by including a non-parametriccomponent to construct a flexible model for modeling various types of covariateeffects. We employ the Bernstein polynomials as the sieve space to approximatethe non-parametric functions so that our method can be implemented easily usingthe existing R packages. Extensive simulation studies suggest that the proposedmethod performs better than other commonly used penalty-based variableselection methods. We apply the method to the CATHGEN data with a binaryresponse from a coronary artery disease study, which motivated our research,and obtained new findings in both high-dimensional genetic and low-dimensionalnon-genetic covariates.

Broken Adaptive Ridge Method for Variable Selection in Generalized Partly Linear Models with Application to the Coronary Artery Disease Data