Simultaneous selection of knots and variables in additive models

초록

Traditional variable selection methods in spline-based additive models treat variables and knots independently, often leading to inefficient model fitting. To overcome these limitations, we introduce a unified approach that simultaneously selects variables and knots by applying the Group Exponential Lasso-a bi-level selection method that selects both variable groups and individual variables within those groups. We first prove the group sparsity and asymptotic normality of Group Exponential Lasso under mild conditions. Utilizing this result, our method achieves the optimal prediction error of standard polynomial spline estimators and asymptotically sets null groups to zero as the sample size increases. Consequently, by eliminating non-significant knots, it streamlines the fitting process and more accurately captures the effects of explanatory variables on the response variable. We also illustrate promising finite-sample performance through both simulation and real data analyses.

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