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 17 articles , 1 standard article )

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  1. Clara Happ: Object-Oriented Software for Functional Data (2017) arXiv
  2. Petrovich, Justin; Reimherr, Matthew: Asymptotic properties of principal component projections with repeated eigenvalues (2017)
  3. Boj, Eva; Caballé, Adrià; Delicado, Pedro; Esteve, Anna; Fortiana, Josep: Global and local distance-based generalized linear models (2016)
  4. Rathnayake, Lasitha N.; Choudhary, Pankaj K.: Tolerance bands for functional data (2016)
  5. Scheipl, Fabian; Gertheiss, Jan; Greven, Sonja: Generalized functional additive mixed models (2016)
  6. Scheipl, Fabian; Greven, Sonja: Identifiability in penalized function-on-function regression models (2016)
  7. Xiao, Luo; Zipunnikov, Vadim; Ruppert, David; Crainiceanu, Ciprian: Fast covariance estimation for high-dimensional functional data (2016)
  8. Goldsmith, Jeff; Zipunnikov, Vadim; Schrack, Jennifer: Generalized multilevel function-on-scalar regression and principal component analysis (2015)
  9. Ivanescu, Andrada E.; Staicu, Ana-Maria; Scheipl, Fabian; Greven, Sonja: Penalized function-on-function regression (2015)
  10. McLean, Mathew W.; Hooker, Giles; Ruppert, David: Restricted likelihood ratio tests for linearity in scalar-on-function regression (2015)
  11. Meyer, Mark J.; Coull, Brent A.; Versace, Francesco; Cinciripini, Paul; Morris, Jeffrey S.: Bayesian function-on-function regression for multilevel functional data (2015)
  12. Reiss, Philip T.; Huo, Lan; Zhao, Yihong; Kelly, Clare; Ogden, R.Todd: Wavelet-domain regression and predictive inference in psychiatric neuroimaging (2015)
  13. Staicu, Ana-Maria; Lu, Xiaosun: Analysis of AneuRisk65 data: classification and curve registration (2014)
  14. Ugarte, Maria D.; Aguilera, Ana M.: More on functional data analysis and other aspects in OODA (2014)
  15. Wang, Wei: Linear mixed function-on-function regression models (2014)
  16. Goldsmith, J.; Greven, S.; Crainiceanu, C.: Corrected confidence bands for functional data using principal components (2013)
  17. Randolph, Timothy W.; Harezlak, Jaroslaw; Feng, Ziding: Structured penalties for functional linear models -- partially empirical eigenvectors for regression (2012)