Simultaneous confidence bands for penalized spline estimators. 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.

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  1. Bao, Junshu; Hanson, Timothy; McMillan, Garnett P.; Knight, Kristin: Assessment of DPOAE test-retest difference curves via hierarchical Gaussian processes (2017)
  2. Holland, Ashley D.: Penalized spline estimation in the partially linear model (2017)
  3. Langrock, Roland; Kneib, Thomas; Glennie, Richard; Michelot, Théo: Markov-switching generalized additive models (2017)
  4. Lu, Xiaolei; Kuriki, Satoshi: Simultaneous confidence bands for contrasts between several nonlinear regression curves (2017)
  5. Hofner, Benjamin; Kneib, Thomas; Hothorn, Torsten: A unified framework of constrained regression (2016)
  6. Michelot, Théo; Langrock, Roland; Kneib, Thomas; King, Ruth: Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models (2016)
  7. Gu, Lijie; Yang, Lijian: Oracally efficient estimation for single-index link function with simultaneous confidence band (2015)
  8. Langrock, Roland; Kneib, Thomas; Sohn, Alexander; DeRuiter, Stacy L.: Nonparametric inference in hidden Markov models using P-splines (2015)
  9. Lim, Yaeji; Oh, Hee-Seok: Simultaneous confidence interval for quantile regression (2015)
  10. Murray, Thomas A.; Hobbs, Brian P.; Carlin, Bradley P.: Combining nonexchangeable functional or survival data sources in oncology using generalized mixture commensurate priors (2015)
  11. Lang, Stefan; Umlauf, Nikolaus; Wechselberger, Peter; Harttgen, Kenneth; Kneib, Thomas: Multilevel structured additive regression (2014)
  12. Li, Gaorong; Peng, Heng; Dong, Kai; Tong, Tiejun: Simultaneous confidence bands and hypothesis testing for single-index models (2014)
  13. Nobles, Mallory; Serban, Nicoleta; Swann, Julie: Spatial accessibility of pediatric primary healthcare: measurement and inference (2014)
  14. Yang, Suigen; Xue, Liugen; Li, Gaorong: Simultaneous confidence band for single-index random effects models with longitudinal data (2014)
  15. Cardot, Hervé; Degras, David; Josserand, Etienne: Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data (2013)
  16. Shang, Zuofeng; Cheng, Guang: Local and global asymptotic inference in smoothing spline models (2013)
  17. De Brabanter, K.; Karsmakers, P.; De Brabanter, J.; Suykens, J.A.K.; De Moor, B.: Confidence bands for least squares support vector machine classifiers: a regression approach (2012)
  18. Wiesenfarth, Manuel; Krivobokova, Tatyana; Klasen, Stephan; Sperlich, Stefan: Direct simultaneous inference in additive models and its application to model undernutrition (2012)
  19. Koenker, Roger: Additive models for quantile regression: model selection and confidence bands (2011)
  20. Sørbye, Sigrunn H.; Rue, Håvard: Simultaneous credible bands for latent Gaussian models (2011)

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