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Simultaneous Confidence Bands for Penalized Spline Estimators

Author

Listed:
  • Tatyana Krivobokova

    (Georg-August-Universität Göttingen)

  • Thomas Kneib

    (Ludwig-Maximilians-Universität München)

  • Gerda Claeskens

    (Katholieke Universiteit Leuven)

Abstract

In this paper we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (i) as a standard (fixed effect) nonparametric model, (ii) using the mixed model framework with the spline coefficients as random effects and (iii) a Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared from a frequentist perspective to Bayesian simultaneous confidence bands. It is shown that the mixed model formulation of penalized splines can help to obtain, at least approximately, confidence bands with either Bayesian or frequentist properties. Simulations and data analysis support the methods proposed. The R package ConfBands accompanies the paper.

Suggested Citation

  • Tatyana Krivobokova & Thomas Kneib & Gerda Claeskens, 2009. "Simultaneous Confidence Bands for Penalized Spline Estimators," Courant Research Centre: Poverty, Equity and Growth - Discussion Papers 12, Courant Research Centre PEG.
    • Handle: RePEc:got:gotcrc:012
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    Keywords

    Bayesian penalized splines; B-splines; Confidence band; Mixed model; Penalization;
    All these keywords.

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