refund swMATH ID: 7434 Software Authors: Goldsmith, J.; Greven, S.; Crainiceanu, C. Description: 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. Homepage: http://cran.r-project.org/web/packages/refund/index.html Source Code: https://github.com/cran/refund Dependencies: R Keywords: bootstrap; functional principal components analysis; iterated expectation and variance; simultaneous bands Related Software: fda (R); R; SemiPar; gamair; mgcv; FDboost; fda.usc; pffr; Matlab; GitHub; orthogonalsplinebasis; GAMLSS; fdasrvf; funHDDC; MFPCA; funFEM; GPFDA; ftsa; Rainbow; WinBUGS Cited in: 62 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Corrected confidence bands for functional data using principal components. Zbl 1274.62776Goldsmith, J.; Greven, S.; Crainiceanu, C. 2013 all top 5 Cited by 112 Authors 14 Greven, Sonja 11 Scheipl, Fabian 9 Crăiniceanu, Ciprian-Mugur 7 Staicu, Ana-Maria 4 Goldsmith, Jeff 4 Ivanescu, Andrada E. 4 Reimherr, Matthew L. 4 Ruppert, David 3 Brockhaus, Sarah 3 Reiss, Philip T. 3 Zipunnikov, Vadim M. 2 Carroll, Raymond James 2 Cederbaum, Jona 2 Checkley, William 2 Coull, Brent A. 2 Cui, Erjia 2 Gellar, Jonathan E. 2 Harezlak, Jaroslaw 2 Hooker, Giles 2 Kowal, Daniel R. 2 Leroux, Andrew 2 Maity, Arnab Kumar 2 Meyer, Mark J. 2 Morris, Jeffrey S. 2 Ogden, Robert Todd 2 Petrovich, Justin 2 Randolph, Timothy W. 2 Shang, Han Lin 2 Smirnova, Ekaterina 2 Xiao, Luo 2 Xu, Meng 1 Aguilera, Ana M. 1 Backenroth, Daniel 1 Bai, Jiawei 1 Bauer, Alexander Max 1 Bharath, Karthik 1 Boj, Eva 1 Bourgeois, Daniel C. 1 Caballé, Adrià 1 Cao, Jiguo 1 Choi, Hyunphil 1 Choudhary, Pankaj K. 1 Ciarleglio, Adam 1 Cinciripini, Paul 1 Coffman, Donna L. 1 Colantuoni, Elizabeth 1 Cortés López, Juan Carlos 1 Delicado, Pedro F. 1 Durban, Maria 1 Dziak, John J. 1 Egan, Joel M. 1 Eilers, Paul H. C. 1 Esteve, Anna 1 Fang, Zhuo 1 Feng, Ziding 1 Fortiana, Josep 1 Fuchs, Karen 1 Gabriel, Alice-Agnes 1 Gertheiss, Jan 1 Guinness, Joseph 1 Happ, Clara 1 Harran, Michelle D. 1 Hoole, Phil 1 Hothorn, Torsten 1 Huo, Lan 1 Johns, Jordan T. 1 Kelly, Clare 1 Khormali, Omid 1 Kim, Janet S. 1 Kitago, Tomoko 1 Krakauer, John W. 1 Küchenhoff, Helmut 1 Kundu, Madan G. 1 Kurtek, Sebastian 1 Lee, Dae-Jin 1 Leisch, Friedrich 1 Li, Cai 1 Li, Meng 1 Li, Runze 1 Lu, Xiaosun 1 Mair, Patrick 1 Malloy, Elizabeth J. 1 Matuk, James 1 McLean, Mathew W. 1 Melcher, Michael 1 Mendoza Benavides, S. M. 1 Mohammed, Shariq 1 Mousavi, Seyed Nourollah 1 Needham, Dale M. 1 Opitz, Madeleine 1 Petkova, Eva 1 Pouplier, Marianne 1 Rathnayake, Lasitha N. 1 Reich, Brian James 1 Rodríguez-Álvarez, María Xosé 1 Roy, Arkaprava 1 Schaffer, Sophia Anna 1 Schrack, Jennifer A. 1 Shiffman, Saul 1 Shinohara, Russell T. ...and 12 more Authors all top 5 Cited in 23 Serials 10 Statistical Modelling 8 Statistics and Computing 6 Biometrics 6 Journal of Computational and Graphical Statistics 4 Electronic Journal of Statistics 3 Computational Statistics and Data Analysis 3 Test 2 Journal of the American Statistical Association 2 Journal of Multivariate Analysis 2 Statistics & Probability Letters 1 Biometrical Journal 1 Journal of Statistical Planning and Inference 1 Computational Statistics 1 Communications in Statistics. Simulation and Computation 1 Journal of Statistical Computation and Simulation 1 Journal of the Royal Statistical Society. Series B. Statistical Methodology 1 Journal of Applied Statistics 1 The Annals of Applied Statistics 1 Statistics Surveys 1 Journal of Agricultural, Biological, and Environmental Statistics 1 Journal of Probability and Statistics 1 Bayesian Analysis 1 Use R! all top 5 Cited in 7 Fields 61 Statistics (62-XX) 6 Numerical analysis (65-XX) 2 Biology and other natural sciences (92-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year