Title: Simultaneous confidence bands for penalized spline estimators
Authors: Krivobokova, Tatyana
Kneib, Thomas
Claeskens, Gerda
Issue Date: Jan-2010
Publisher: K.U.Leuven - Faculty of Business and Economics
Series Title: FBE Research Report KBI_1001
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 full 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.
Publication status: published
KU Leuven publication type: IR
Appears in Collections:Research Center for Operations Research and Business Statistics (ORSTAT), Leuven

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