R package refund: Regression with Functional Data. Corrected confidence bands for functional data using principal components. Functional principal components (FPC) analysis is widely used to decompose and express functional observations. Curve estimates implicitly condition on basis functions and other quantities derived from FPC decompositions; however these objects are unknown in practice. In this article, we propose a method for obtaining correct curve estimates by accounting for uncertainty in FPC decompositions. Additionally, pointwise and simultaneous confidence intervals that account for both model- and decomposition-based variability are constructed. Standard mixed model representations of functional expansions are used to construct curve estimates and variances conditional on a specific decomposition. Iterated expectation and variance formulas combine model-based conditional estimates across the distribution of decompositions. A bootstrap procedure is implemented to understand the uncertainty in principal component decomposition quantities. Our method compares favorably to competing approaches in simulation studies that include both densely and sparsely observed functions. We apply our method to sparse observations of CD4 cell counts and to dense white-matter tract profiles. Code for the analyses and simulations is publicly available, and our method is implemented in the R package refund on CRAN.

References in zbMATH (referenced in 65 articles , 1 standard article )

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  1. Hooker, Giles; Shang, Han Lin: Selecting the derivative of a functional covariate in scalar-on-function regression (2022)
  2. Li, Meng; Wang, Kehui; Maity, Arnab; Staicu, Ana-Maria: Inference in functional linear quantile regression (2022)
  3. Cui, Erjia; Crainiceanu, Ciprian M.; Leroux, Andrew: Additive functional Cox model (2021)
  4. Evandro Konzen, Yafeng Cheng, Jian Qing Shi: Gaussian Process for Functional Data Analysis: The GPFDA Package for R (2021) arXiv
  5. Kowal, Daniel R.: Dynamic regression models for time-ordered functional data (2021)
  6. Meyer, Mark J.; Malloy, Elizabeth J.; Coull, Brent A.: Bayesian wavelet-packet historical functional linear models (2021)
  7. Roy, Arkaprava; Reich, Brian J.; Guinness, Joseph; Shinohara, Russell T.; Staicu, Ana-Maria: Spatial shrinkage via the product independent Gaussian process prior (2021)
  8. Steven Golovkine: FDApy: a Python package for functional data (2021) arXiv
  9. Stöcker, Almond; Brockhaus, Sarah; Schaffer, Sophia Anna; von Bronk, Benedikt; Opitz, Madeleine; Greven, Sonja: Boosting functional response models for location, scale and shape with an application to bacterial competition (2021)
  10. Zhou, Zhiyang: Fast implementation of partial least squares for function-on-function regression (2021)
  11. Barinder Thind, Sidi Wu, Richard Groenewald, Jiguo Cao: FuncNN: An R Package to Fit Deep Neural Networks Using Generalized Input Spaces (2020) arXiv
  12. Greven, Sonja; Scheipl, Fabian: Comments on: “Inference and computation with generalized additive models and their extensions” (2020)
  13. Kowal, Daniel R.; Bourgeois, Daniel C.: Bayesian function-on-scalars regression for high-dimensional data (2020)
  14. Matuk, James; Mohammed, Shariq; Kurtek, Sebastian; Bharath, Karthik: Biomedical applications of geometric functional data analysis (2020)
  15. Reiss, Philip T.; Xu, Meng: Tensor product splines and functional principal components (2020)
  16. Xu, Meng; Reiss, Philip T.: Distribution-free pointwise adjusted (p)-values for functional hypotheses (2020)
  17. Cao, Jiguo; Soiaporn, Kunlaya; Carroll, Raymond J.; Ruppert, David: Modeling and prediction of multiple correlated functional outcomes (2019)
  18. Dziak, John J.; Coffman, Donna L.; Reimherr, Matthew; Petrovich, Justin; Li, Runze; Shiffman, Saul; Shiyko, Mariya P.: Scalar-on-function regression for predicting distal outcomes from intensively gathered longitudinal data: interpretability for applied scientists (2019)
  19. Johns, Jordan T.; Crainiceanu, Ciprian; Zipunnikov, Vadim; Gellar, Jonathan: Variable-domain functional principal component analysis (2019)
  20. Park, S. Y.; Li, C.; Mendoza Benavides, S. M.; van Heugten, E.; Staicu, A. M.: Conditional analysis for mixed covariates, with application to feed intake of lactating sows (2019)

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