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A unified framework for spline estimators

Author

Listed:
  • Katsiaryna Schwarz

    (Georg-August-University Göttingen)

  • Tatyana Krivobokova

    (Georg-August-University Göttingen)

Abstract

This article develops a unified framework to study the (asymptotic) properties of (periodic) spline based estimators, that is of regression, penalized and smoothing splines. We obtain an explicit form of the Demmler-Reinsch basis of general degree in terms of exponential splines and corresponding eigenvalues by applying Fourier techniques to periodic smoothers. This allows to derive exact expressions for the equivalent kernels of all spline estimators and get insights into the local and global asymptotic behavior of these estimators.

Suggested Citation

  • Katsiaryna Schwarz & Tatyana Krivobokova, 2012. "A unified framework for spline estimators," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 130, Courant Research Centre PEG.
    • Handle: RePEc:got:gotcrc:130
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    File URL: http://www2.vwl.wiso.uni-goettingen.de/courant-papers/CRC-PEG_DP_130.pdf
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    Keywords

    B-splines; Equivalent kernels; Euler-Frobenius polynomials; Exponential splines; Demmler-Reinsch basis;
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