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Robust penalized spline estimation with difference penalties

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  • Kalogridis, Ioannis
  • Van Aelst, Stefan

Abstract

Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model assumptions. To remedy this deficiency, a broad class of P-spline estimators based on general loss functions is introduced and studied. Robust estimators are obtained by well-chosen loss functions, such as the Huber or Tukey loss function. A preliminary scale estimator can also be included in the loss function. It is shown that this class of P-spline estimators enjoys the same optimal asymptotic properties as least-squares P-splines, thereby providing strong theoretical motivation for its use. The proposed estimators may be computed very efficiently through a simple adaptation of well-established iterative least squares algorithms and exhibit excellent performance even in finite samples, as evidenced by a numerical study and a real-data example.

Suggested Citation

  • Kalogridis, Ioannis & Van Aelst, Stefan, 2024. "Robust penalized spline estimation with difference penalties," Econometrics and Statistics, Elsevier, vol. 29(C), pages 169-188.
    • Handle: RePEc:eee:ecosta:v:29:y:2024:i:c:p:169-188
    DOI: 10.1016/j.ecosta.2021.07.005
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    References listed on IDEAS

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