Simultaneous Confidence Bands for Penalized Spline Estimators

Tatyana Krivobokova, Thomas Kneib and Gerda Claeskens
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Tatyana Krivobokova: Georg-August-Universität Göttingen
Thomas Kneib: Ludwig-Maximilians-Universität München
Gerda Claeskens: Katholieke Universiteit Leuven

No 12, Courant Research Centre: Poverty, Equity and Growth - Discussion Papers from Courant Research Centre PEG

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.

Keywords: Bayesian penalized splines; B-splines; Confidence band; Mixed model; Penalization (search for similar items in EconPapers)
Date: 2009-09-01
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Persistent link: https://EconPapers.repec.org/RePEc:got:gotcrc:012

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