Estimator selection and combination in scalar-on-function regression

• Published in: Computational statistics & data analysis 2014-02, Vol.70, p.362-372
• Main Authors: Goldsmith, Jeff, Scheipl, Fabian
• Format: Article
• Language: English
• Subjects: Benchmarking; Collection; Cross validation; Data processing; Estimators; Functional linear model; Mathematical models; Model stacking; Regression; Statistics; Super learning; Tuning
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2013.10.009

Scalar-on-function regression problems with continuous outcomes arise naturally in many settings, and a wealth of estimation methods now exist. Despite the clear differences in regression model assumptions, tuning parameter selection, and the incorporation of functional structure, it remains common to apply a single method to any dataset of interest. In this paper we develop tools for estimator selection and combination in the context of continuous scalar-on-function regression based on minimizing the cross-validated prediction error of the final estimator. A broad collection of functional and high-dimensional regression methods is used as a library of candidate estimators. We find that the performance of any single method relative to others can vary dramatically across datasets, but that the proposed cross-validation procedure is consistently among the top performers. Four real-data analyses using publicly available benchmark datasets are presented; code implementing these analyses and facilitating the application of proposed methods on future datasets is available in a web supplement.