Adaptive empirical Bayesian smoothing splines

TL;DR

This paper introduces adaptive empirical Bayesian smoothing splines that automatically select smoothing parameters and penalty order, providing credible sets with reliable coverage and outperforming traditional methods.

Contribution

It develops a novel adaptive empirical Bayesian approach for smoothing splines that jointly determines the smoothing parameter and penalty order from data.

Findings

Adaptive credible sets with good frequentist coverage

Superior performance over frequentist smoothing splines

Joint selection of smoothing parameter and penalty order

Abstract

In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the model. The selected order and smoothing parameter are used to construct adaptive credible sets with good frequentist coverage for the underlying regression function. We use these credible sets as a proxy to show the superior performance of adaptive empirical Bayesian smoothing splines compared to frequentist smoothing splines.