Simultaneous Confidence Bands for Penalized Spline Estimators

• 成果类型: Article
• 署名作者: Krivobokova, Tatyana; Kneib, Thomas; Claeskens, Gerda
• 署名单位: University of Gottingen; University of Gottingen; Carl von Ossietzky Universitat Oldenburg; KU Leuven; KU Leuven
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2010.tm09165
• 发表日期: 2010
• 页码: 852-863
• 关键词: structured additive regression; Nonparametric Regression; heteroscedastic errors; linear-regression; CURVES; tubes; asymptotics; inference; THEOREM; volume

摘要

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.