ConfBands

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.


References in zbMATH (referenced in 31 articles , 1 standard article )

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  1. Gu, Lijie; Wang, Suojin; Yang, Lijian: Smooth simultaneous confidence band for the error distribution function in nonparametric regression (2021)
  2. Delaigle, Aurore; Huang, Wei; Lei, Shaoke: Estimation of conditional prevalence from group testing data with missing covariates (2020)
  3. Yoshida, Takuma: Simultaneous confidence bands for extremal quantile regression with splines (2020)
  4. Yu, Shan; Wang, Guannan; Wang, Li; Liu, Chenhui; Yang, Lijian: Estimation and inference for generalized geoadditive models (2020)
  5. Hui, Francis K. C.; You, C.; Shang, H. L.; Müller, Samuel: Semiparametric regression using variational approximations (2019)
  6. Bauer, Alexander; Scheipl, Fabian; Küchenhoff, Helmut; Gabriel, Alice-Agnes: An introduction to semiparametric function-on-scalar regression (2018)
  7. Pütz, Peter; Kneib, Thomas: A penalized spline estimator for fixed effects panel data models (2018)
  8. Bao, Junshu; Hanson, Timothy; McMillan, Garnett P.; Knight, Kristin: Assessment of DPOAE test-retest difference curves via hierarchical Gaussian processes (2017)
  9. Holland, Ashley D.: Penalized spline estimation in the partially linear model (2017)
  10. Langrock, Roland; Kneib, Thomas; Glennie, Richard; Michelot, Théo: Markov-switching generalized additive models (2017)
  11. Lu, Xiaolei; Kuriki, Satoshi: Simultaneous confidence bands for contrasts between several nonlinear regression curves (2017)
  12. Hofner, Benjamin; Kneib, Thomas; Hothorn, Torsten: A unified framework of constrained regression (2016)
  13. Michelot, Théo; Langrock, Roland; Kneib, Thomas; King, Ruth: Maximum penalized likelihood estimation in semiparametric mark-recapture-recovery models (2016)
  14. Gu, Lijie; Yang, Lijian: Oracally efficient estimation for single-index link function with simultaneous confidence band (2015)
  15. Langrock, Roland; Kneib, Thomas; Sohn, Alexander; DeRuiter, Stacy L.: Nonparametric inference in hidden Markov models using P-splines (2015)
  16. Lim, Yaeji; Oh, Hee-Seok: Simultaneous confidence interval for quantile regression (2015)
  17. Murray, Thomas A.; Hobbs, Brian P.; Carlin, Bradley P.: Combining nonexchangeable functional or survival data sources in oncology using generalized mixture commensurate priors (2015)
  18. Lang, Stefan; Umlauf, Nikolaus; Wechselberger, Peter; Harttgen, Kenneth; Kneib, Thomas: Multilevel structured additive regression (2014)
  19. Li, Gaorong; Peng, Heng; Dong, Kai; Tong, Tiejun: Simultaneous confidence bands and hypothesis testing for single-index models (2014)
  20. Nobles, Mallory; Serban, Nicoleta; Swann, Julie: Spatial accessibility of pediatric primary healthcare: measurement and inference (2014)

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