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Discussion of: “A general framework for functional regression modelling”. (English) Zbl 07289475

Summary: This discussion provides our reaction to the article by Greven and Scheipl [Stat. Model. 17, No. 1–2, 1–35 (2017; Zbl 07289474)]. It contains an overview of their article and a description of the many areas of research that remain open and could benefit from further methodological and computational development.

MSC:

62-XX Statistics

Citations:

Zbl 07289474
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[1] Adler, D, Kneib, T, Lang, S, Umlauf, N, Zeileis, A (2013) BayesXsrc: R package distribution of the BayesX C++ sources, R package ver- sion 2.1-2., URL http://CRAN.R-project.org/package=BayesXsrc (last accessed 6 January 2017).
[2] Allen, G, Grosenick, L, Taylor, J (2014) A generalized least squares matrix decomposition. Journal of the American Statistical Association, 109, 145-59. · Zbl 1367.62184 · doi:10.1080/01621459.2013.852978
[3] Belitz, C, Brezger, A, Kneib, T, Lang, S, Umlauf, N (2013) BayesX: Software for Bayesian inference in structured additive regression models, Version 2.1., URL http://www.BayesX.org/ (last accessed 6 January 2017).
[4] Chen, Y, Goldsmith, J, Ogden, T (2016) A generalized least squares matrix decomposition. Variable Selection in Function-on-Scalar Regression, 5, 88-101.
[5] Crainiceanu, C, Caffo, B, Di, C, Punjabi, N (2009) Nonparametric signal extraction and measurement error in the analysis of electroencephalographic data. Journal of the American Statistical Association, 104, 541-55. · Zbl 1388.62316 · doi:10.1198/jasa.2009.0020
[6] Di, C, Crainiceanu, B, Punjabi, N (2009) Multilevel functional principal component analysis. The Annals of Applied Statistics, 3, 458-88. · Zbl 1160.62061 · doi:10.1214/08-AOAS206
[7] Di, C, Crainiceanu, C, Jank, W (2014) Multi- level sparse functional principal component analysis. Stat, 3, 126-43. doi 10.1002/sta4.50. URL http://dx.doi.org/10.1002/sta4.50 (last accessed 6 January 2017). · doi:10.1002/sta4.50
[8] Dien, J, Spencer, K, Donchin, E (2003) Localization of the event-related potential novelty response as deffined by principal components analysis. Cognitive Brain Research, 17, 637-50. · doi:10.1016/S0926-6410(03)00188-5
[9] Eilers, P, Marx, B (1996) Flexible smoothing with b-splines and penalties. Statistical Science, 11, 89-121. · Zbl 0955.62562 · doi:10.1214/ss/1038425655
[10] Eilers, P, Marx, B (2002) Generalized linear additive smooth structures. Journal of Computational and Graphical Statistics, 11,758-83. · doi:10.1198/106186002844
[11] Eilers, P, Marx, B (2003) Multivariate calibra-tion with temperature interaction using two-dimensional penalized signal regression. Chemometrics and intelligent laboratory systems, 66, 159-74. · doi:10.1016/S0169-7439(03)00029-7
[12] Gellar, J, Colantuoni, E, Needham, D, Crainiceanu, C (2014) Variable-domain functional regression for modeling icu data. Journal of the American Statistical Association, 109, 1425-39. · doi:10.1080/01621459.2014.940044
[13] Gellar, J, Coljantuoni, E, Needham, D, Crainiceanu, C (2015) Cox regression models with functional covariates for survival data. Statistical modelling, 15, 256-78. · Zbl 07258989
[14] Gertheiss, J, Maity, A, Staicu, AM (2013) Variable selection in generalized functional linear model. Stat, 2, 86-101. · doi:10.1002/sta4.20
[15] Goldsmith, J, Kitago, T (2015) Assessing systematic effects of stroke on motor control using hierarchical function-on-scalar regression. Journal of the Royal Statistical Society: Series C, 65, 215-36. · doi:10.1111/rssc.12115
[16] Huang, L, Reiss, P, Xiao, L, Zipunnikov, V, Lindquist, M, Crainiceanu, C (2016a) Two-way principal component analysis for matrix-variate data, with an application to functional magnetic resonance imaging data. Biostatistics. Available at https://www.ncbi.nlm.nih.gov/pubmed/27578805 · doi:10.1093/biostatistics/kxw040
[17] Huang, L, Scheipl, F, Goldsmith, J, Gellar, J, Harezlak, J, McLean, M, Swihart, B, Xiao, L, Crainiceanu, C, Reiss, P (2016b). Refund: Regression with functional data. URL https://CRAN.R-project.org/package=refund. R.
[18] Ivanescu, A, Staicu, AM, Scheipl, F, Greven, S (2015) Penalized function-on-function regression. Computational Statistics, 30, 539-68. · Zbl 1317.65037 · doi:10.1007/s00180-014-0548-4
[19] James, G, Hastie, T, Sugar, C (2000) Principal component models for sparse functional data. Biometrika, 87, 587-602. · Zbl 0962.62056 · doi:10.1093/biomet/87.3.587
[20] Jiang, CR, Wang, JL (2011) Functional single index models for longitudinal data. The Annals of Statistics, 39, 362-88. · Zbl 1209.62073 · doi:10.1214/10-AOS845
[21] Kitago, T, Goldsmith, J, Harran, M, Kane, L, Berard, J, Huang, S, Ryan, S, Mazzoni, P, Krakauer, J, Huang, V (2015) Robotic therapy for chronic stroke: general recovery of impairment or improved task-specific skill? Journal of Neurophysiology, 114, 1885-94. · doi:10.1152/jn.00336.2015
[22] Kong, D, Staicu, A, Maity, A (2016) Classical testing in functional linear models. Journal of Nonparametric Statistics, 28, 813-38. · Zbl 1348.62136 · doi:10.1080/10485252.2016.1231806
[23] Koster, A, Caserotti, P, Patel, K, Matthews, C, Berrigan, D, Van Domelen, D (2012) Association of sedentary time with mortality independent of moderate to vigorous physical activity. PLoS ONE, 7(6):e37696. Doi:10.1371/journal.pone.0037696. · doi:10.1371/journal.pone.0037696
[24] Li, Y, Wang, N, Carroll, R (2010) Generalized functional linear models with semiparametric single-index interactions. Journal of the American Statistical Association, 105, 621-33. · Zbl 1392.62095 · doi:10.1198/jasa.2010.tm09313
[25] Lindquist, M (2008) The statistical analysis of fMRI data. Statistical Science, 23, 439-64. · Zbl 1329.62296 · doi:10.1214/09-STS282
[26] Ma, S (2016) Estimation and inference in functional single-index models. Annals of the Institute of Statistical Mathematics, 68, 181-208. · Zbl 1440.62132 · doi:10.1007/s10463-014-0488-3
[27] O’Sullivan, F (1986) A statistical perspective on ill-posed inverse problems. Statistical Science, 1, 502-18. · Zbl 0625.62110 · doi:10.1214/ss/1177013525
[28] Plummer, M (2003) JAGS: a program for analysis of Bayesian graphical models using Gibbs sampling. In Hornik, K, Leisch, F, Zeileis, A (eds) Proceedings of the 3rd International Workshop on Distributed Sta- tistical Computing (DSC 2003), Vienna. Available at https://www.r-project.org/conferences/DSC-2003/Drafts/Plummer.pdf
[29] Quan, S, Howard, B, Iber, C, Kiley, J, Nieto, F, OConnor, G, Rapoport, D, Redline, S, Robbins, J, Samet, J, Wahl, PW (1997). The sleep heart health study: Design, rationale, and methods. Sleep, 20, 1077-85.
[30] R Core Team (2014) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/ (last accessed 6 January 2017).
[31] Reiss, P, Ogden, R (2007) Functional principal component regression and functional partial least squares. Journal of the American Statistical Association, 102, 984-96. · Zbl 1469.62237 · doi:10.1198/016214507000000527
[32] Ruppert, D, Wand, M, Carroll, R (2003) Semiparametric regression. Cambridge: Cambridge University Press. · Zbl 1038.62042 · doi:10.1017/CBO9780511755453
[33] Scheipl, F, Staicu, AM, Greven, S (2015) Functional additive mixed models. Journal of Computational and Graphical Statistics, 24, 477-501. · Zbl 1430.62082 · doi:10.1080/10618600.2014.901914
[34] Schrack, J, Zipunnikov, V, Goldsmith, J, Bai, J, Simonsick, E, Crainiceanu, C, Ferrucci, L (2014) Assessing the physical cliff: Detailed quantification of age-related differences in daily patterns of physical activity. Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 69, 973-79. · doi:10.1093/gerona/glt199
[35] Smilde, A, Jansen, JJHH, Lamers, RJ, Van Der Greef, J, Timmerman, M (2005) Anova-simultaneous component analysis (ASCA): A new tool for analyzing designed metabolomics data. Bioinformatics, 21, 3043-48. · doi:10.1093/bioinformatics/bti476
[36] Spencer, K, Dien, J, Donchin, E (2001) Spatiotemporal analysis of the late erp responses to deviant stimuli. Psychophy-siology, 38, 343-58. · doi:10.1111/1469-8986.3820343
[37] Staicu, AM, Crainiceanu, C, Reich, DS, Ruppert, D (2012) Modeling functional data with spatially heterogeneous shape characteristics. Biometrics, 68, 331-43. · Zbl 1251.62050 · doi:10.1111/j.1541-0420.2011.01669.x
[38] Staicu, AM, Serban, N, Carroll, RJ (2015) Significance tests for functional data with complex dependence structure. Journal of Statistical Planning and Inference, 156, 1-13. · Zbl 1307.62128 · doi:10.1016/j.jspi.2014.08.006
[39] Stone, J, Norris, A (1966) Activities and attitudes of participants in the Baltimore longitudinal study. Journal of Gerontology, 21, 575-80. · doi:10.1093/geronj/21.4.575
[40] Swihart, B, Goldsmith, J, Crainiceanu, C (2014) Restricted likelihood ratio tests for functional effects in the functional linear model. Technometrics, 56, 483-93. · doi:10.1080/00401706.2013.863163
[41] Troiano, R, Berrigan, D, Dodd, K, Msse, L, Tilert, T, McDowell, M (2008) Physical activity in the united states measured by accelerometer. Medicine & Science in Sports & Exercise, 40, 181-88. · doi:10.1249/mss.0b013e31815a51b3
[42] Tseng, YK, Hsieh, F, Wang, JL (2005) Joint modelling of accelerated failure time and longitudinal data. Biometrika, 92, 587-603. · Zbl 1152.62380 · doi:10.1093/biomet/92.3.587
[43] Tsiatis, A, Davidian, M (2004) Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica, 14, 809-34. · Zbl 1073.62087
[44] Wood, S (2000) Modelling and smoothing parameter estimation with multiple quadratic penalties. Journal of the Royal Statistical Society (B), 62, 413-28. · doi:10.1111/1467-9868.00240
[45] Wood, S (2003) Thin-plate regression splines. Journal of the Royal Statistical Society (B), 65, 95-114. · Zbl 1063.62059 · doi:10.1111/1467-9868.00374
[46] Wood, S (2004) Stable and efficient multiple smoothing parameter estimation for generalized additive models. Journal of the American Statistical Association, 99, 673-86. · Zbl 1117.62445 · doi:10.1198/016214504000000980
[47] Wood, S (2006) Generalized additive models: An introduction with R. Boca Raton, FL: Chapman & Hall CRC. · Zbl 1087.62082
[48] Wood, S (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B), 73, 3-36. · Zbl 1411.62089 · doi:10.1111/j.1467-9868.2010.00749.x
[49] Yao, F, Mller, HG, Wang, J (2005) Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100, 577-90. · Zbl 1117.62451 · doi:10.1198/016214504000001745
[50] Zhang, JT, Chen, J (2007) Statistical inferences for functional data. The Annals of Statistics, 35, 1052-79. · Zbl 1129.62029 · doi:10.1214/009053606000001505
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