A sparse multivariate nonparametric regression for high-dimensional data via the elastic-net penalty

The Component Selection and Smoothing Operator (COSSO) is a nonparametric regression model based on smoothing spline ANOVA that simultaneously estimates and selects main effects and interaction components. However, the original COSSO is designed for low-dimensional settings and encounters challenges when applied to high-dimensional data. This study extends COSSO to accommodate high-dimensional contexts by incorporating an elastic-net type penalty, which enables stable component selection even in the presence of highly correlated variables. In addition, COSSO is generalized within the framework of generalized linear models, allowing its application to exponential family distributions and the Cox proportional hazards model. A coordinate descent algorithm is employed for efficient computation. Simulation studies and real data analyses demonstrate that the proposed method outperforms existing approaches in terms of both selection accuracy and stability.