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A unified framework for spline estimators

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  • Katsiaryna Schwarz
  • Tatyana Krivobokova

Abstract

This article develops a unified framework to study the asymptotic properties of all periodic spline-based estimators, that is, of regression, penalized and smoothing splines. The explicit form of the periodic Demmler–Reinsch basis in terms of exponential splines allows the derivation of an expression for the asymptotic equivalent kernel on the real line for all spline estimators simultaneously. The corresponding bandwidth, which drives the asymptotic behaviour of spline estimators, is shown to be a function of the number of knots and the smoothing parameter. Strategies for the selection of the optimal bandwidth and other model parameters are discussed.

Suggested Citation

  • Katsiaryna Schwarz & Tatyana Krivobokova, 2016. "A unified framework for spline estimators," Biometrika, Biometrika Trust, vol. 103(1), pages 121-131.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:1:p:121-131.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv070
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    Cited by:

    1. Yakun Wang & Zeda Li & Scott A. Bruce, 2023. "Adaptive Bayesian sum of trees model for covariate‐dependent spectral analysis," Biometrics, The International Biometric Society, vol. 79(3), pages 1826-1839, September.
    2. Sebastian Letmathe & Yuanhua Feng, 2022. "An iterative plug-in algorithm for P-Spline regression," Working Papers CIE 151, Paderborn University, CIE Center for International Economics.
    3. Scott A. Bruce & Martica H. Hall & Daniel J. Buysse & Robert T. Krafty, 2018. "Conditional adaptive Bayesian spectral analysis of nonstationary biomedical time series," Biometrics, The International Biometric Society, vol. 74(1), pages 260-269, March.

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