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- Publisher
- Taylor & Francis
- Copyright
- © 2010 American Statistical Association
- ISSN
- 1537-274X
- eISSN
- 0162-1459
- DOI
- 10.1198/jasa.2010.tm09165
- Publisher site
- See Article on Publisher Site
Abstract
In this article we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (a) as a standard (fixed effect) nonparametric model, (b) using the mixed-model framework with the spline coefficients as random effects, and (c) a full Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared with Bayesian simultaneous confidence bands from a frequentist perspective. We show that the mixed-model formulation of penalized splines can help obtain, at least approximately, confidence bands with either Bayesian or frequentist properties. Simulations and data analysis support the proposed methods. The R package ConfBands accompanies the article.
Journal
Journal of the American Statistical Association – Taylor & Francis
Published: Jun 1, 2010
Keywords: B-spline; Bayesian penalized spline; Confidence band; Mixed model; Penalization