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 39 articles , 1 standard article )

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  1. Matuk, James; Mohammed, Shariq; Kurtek, Sebastian; Bharath, Karthik: Biomedical applications of geometric functional data analysis (2020)
  2. Reiss, Philip T.; Xu, Meng: Tensor product splines and functional principal components (2020)
  3. Xu, Meng; Reiss, Philip T.: Distribution-free pointwise adjusted (p)-values for functional hypotheses (2020)
  4. Cao, Jiguo; Soiaporn, Kunlaya; Carroll, Raymond J.; Ruppert, David: Modeling and prediction of multiple correlated functional outcomes (2019)
  5. 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)
  6. 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)
  7. Reimherr, Matthew: Comments on “Modular regression -- a Lego system for building structured additive distributional regression models with tensor product interactions” (2019)
  8. Rodríguez-Álvarez, María Xosé; Durban, Maria; Lee, Dae-Jin; Eilers, Paul H. C.: On the estimation of variance parameters in non-standard generalised linear mixed models: application to penalised smoothing (2019)
  9. Backenroth, Daniel; Goldsmith, Jeff; Harran, Michelle D.; Cortes, Juan C.; Krakauer, John W.; Kitago, Tomoko: Modeling motor learning using heteroscedastic functional principal components analysis (2018)
  10. Cederbaum, Jona; Scheipl, Fabian; Greven, Sonja: Fast symmetric additive covariance smoothing (2018)
  11. Choi, Hyunphil; Reimherr, Matthew: A geometric approach to confidence regions and bands for functional parameters (2018)
  12. Happ, Clara; Greven, Sonja: Multivariate functional principal component analysis for data observed on different (dimensional) domains (2018)
  13. Mair, Patrick: Modern psychometrics with R (2018)
  14. Mousavi, Seyed Nourollah; Sørensen, Helle: Functional logistic regression: a comparison of three methods (2018)
  15. Shang, Han Lin: Bootstrap methods for stationary functional time series (2018)
  16. Xiao, Luo; Li, Cai; Checkley, William; Crainiceanu, Ciprian: Fast covariance estimation for sparse functional data (2018)
  17. Brockhaus, Sarah; Melcher, Michael; Leisch, Friedrich; Greven, Sonja: Boosting flexible functional regression models with a high number of functional historical effects (2017)
  18. Clara Happ: Object-Oriented Software for Functional Data (2017) arXiv
  19. Petrovich, Justin; Reimherr, Matthew: Asymptotic properties of principal component projections with repeated eigenvalues (2017)
  20. Boj, Eva; Caballé, Adrià; Delicado, Pedro; Esteve, Anna; Fortiana, Josep: Global and local distance-based generalized linear models (2016)

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