Simultaneous Confidence Bands for Penalized Spline Estimators
2010 | journal article
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Details
- Authors
- Krivobokova, Tatyana ; Kneib, Thomas ; Claeskens, Gerda
- 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.
- Issue Date
- 2010
- Publisher
- Informa UK Limited
- Journal
- Journal of the American Statistical Association
- ISSN
- 0162-1459