Smoothly adaptively centered ridge estimator

Abstract

With a focus on linear models with smooth functional covariates, we propose a penalization framework (SACR) based on the nonzero centered ridge, where the center of the penalty is adaptively reweighted, starting from the ordinary ridge solution as the initial center. In particular, we introduce a convex formulation that jointly estimates the model’s coefficients and the weight function, with a roughness penalty on the center, and constraints on the weights in order to recover a possibly smooth and/or sparse solution. This allows for a non-iterative and continuous variable selection mechanism, as the weight function can either inflate or deflate the initial center, reducing the unwanted shrinkage on some of the coefficients. As empirical evidence of the interpretability and predictive power of our method, we provide a simulation study and two real world spectroscopy applications, with both classification and regression.