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Estimator selection and combination in scalar-on-function regression

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  • Goldsmith, Jeff
  • Scheipl, Fabian

Abstract

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.

Suggested Citation

  • Goldsmith, Jeff & Scheipl, Fabian, 2014. "Estimator selection and combination in scalar-on-function regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 362-372.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:362-372
    DOI: 10.1016/j.csda.2013.10.009
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    7. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.

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