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Robust functional linear regression based on splines

Authors
Journal
Computational Statistics & Data Analysis
0167-9473
Publisher
Elsevier
Volume
65
Identifiers
DOI: 10.1016/j.csda.2011.11.014
Keywords
  • Mm Estimate
  • Natural Splines
  • Robust Ridge Estimator
Disciplines
  • Computer Science

Abstract

Abstract Many existing methods for functional regression are based on the minimization of an L2 norm of the residuals and are therefore sensitive to atypical observations, which may affect the predictive power and/or the smoothness of the resulting estimate. A robust version of a spline-based estimate is presented, which has the form of an MM estimate, where the L2 loss is replaced by a bounded loss function. The estimate can be computed by a fast iterative algorithm. The proposed approach is compared, with favorable results, to the one based on L2 and to both classical and robust Partial Least Squares through an example with high-dimensional real data and a simulation study.11 Matlab code for the proposed procedure is provided as supplemental material.

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