Methods for Scalar‐on‐Function Regression

International Statistical Review - Tập 85 Số 2 - Trang 228-249 - 2017
Philip T. Reiss1,2,3, Jeff Goldsmith4, Han Lin Shang5, R. Todd Ogden4,6
1Department of Child and Adolescent Psychiatry, New York University School of Medicine, New York, NY, USA
2Department of Population Health, New York University School of Medicine, New York, NY, USA
3Department of Statistics, University of Haifa, Haifa, Israel
4Department of Biostatistics, Columbia University Mailman School of Public Health, New York, NY, USA
5Research School of Finance, Actuarial Studies and Statistics, Australian National University, Canberra, Australia
6New York State Psychiatric Institute, New York, NY, USA

Tóm tắt

SummaryRecent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images and so on are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorising the basic model types as linear, non‐linear and non‐parametric. We discuss publicly available software packages and illustrate some of the procedures by application to a functional magnetic resonance imaging data set.

Từ khóa


Tài liệu tham khảo

10.1016/j.chemolab.2010.09.007

10.1007/s11749-012-0307-1

10.1080/02331880801980377

10.1016/j.csda.2004.12.007

10.1007/978-3-7908-2736-1_2

10.1016/j.spl.2005.12.007

10.1016/j.jmva.2007.04.010

10.1007/s11634-013-0127-5

10.1016/j.jmva.2008.03.008

10.1080/10485250903089930

10.1016/j.csda.2009.09.010

10.1198/016214501753168118

10.1080/02331888.2014.993986

10.1080/10485250802668909

10.1214/009053606000000830

10.1080/01621459.2012.716337

10.1080/10485250500303015

10.1111/1467-9469.00329

10.1016/S0167-7152(99)00036-X

Cardot H., 2003, Spline estimators for the functional linear model, Stat. Sin., 13, 571

Cardot H., 2011, The Oxford Handbook of Functional Data Analysis

10.1214/11-AOS882

10.1111/j.1467-9868.2011.01008.x

10.1007/s00180-014-0503-4

10.1016/j.csda.2014.11.017

10.18637/jss.v032.i11

10.1198/jasa.2009.tm08564

10.1214/07-AOS563

Craven P., 1979, Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross‐validation, Numer. Math., 31, 317

10.1016/j.jspi.2013.04.002

10.1214/11-AOS958

10.1214/09-EJS379

10.1016/j.jmva.2010.10.003

10.1214/08-AOAS206

10.1214/12-AOS1027

10.1007/BF02288367

10.1016/j.chemolab.2009.02.001

10.1198/106186002844

10.1016/j.csda.2006.08.011

Fan J., 1996, Local Polynomial Modelling and its Applications.

10.1214/15-AOS1346

10.1080/10618600.2012.672097

10.1111/insr.12116

10.1007/s11749-012-0308-0

10.18637/jss.v051.i04

10.1007/s11749-012-0306-2

10.1093/biomet/asq058

10.1016/j.crma.2005.01.016

10.1111/j.1467-842X.2007.00480.x

10.1007/978-3-7908-2736-1_17

Ferraty F., 2005, Conditional quantiles for dependent functional data with application to the climatic El Niño phenomenon, Sankhyā: The Indian Journal of Statistics, 67, 378

10.1007/s001800200126

Ferraty F., 2006, Nonparametric Functional Data Analysis: Theory and Practice.

Ferraty F., Additive prediction and boosting for functional data, Comput. Stat. Data Anal., 53, 1400, 10.1016/j.csda.2008.11.023

Ferraty F., 2011, The Oxford Handbook of Functional Data Analysis

10.1080/0233188031000112845

Ferré L., 2005, Smoothed functional inverse regression, Stat. Sin., 15, 665

10.1016/j.chemolab.2015.04.019

10.1080/10618600.2013.812519

10.1214/09-SS049

10.1016/j.spl.2015.09.015

10.1093/biostatistics/kxs051

10.1002/sta4.20

10.1198/jcgs.2010.10007

10.1111/j.1467-9876.2011.01031.x

10.1080/10618600.2012.743437

10.1016/j.csda.2013.10.009

10.1214/11-EJS619

10.1111/1467-9868.00111

10.1214/10-EJS575

10.1007/978-1-4614-5369-7

10.1080/10485250903323180

10.1214/009053606000000957

10.1214/09-AOS686

10.1111/j.1467-9868.2006.00562.x

Härdle W., 2013, Nonparametric and Semiparametric Models

Hastie T., 1993, Discussion of a statistical view of some chemometrics regression tools by by I.E. Frank and J.H. Friedman, Technometrics, 35, 140, 10.2307/1269658

Hastie T., 1990, Generalized Additive Models.

10.1002/asmb.1954

10.1111/j.1541-0420.2009.01331.x

10.1007/978-1-4614-3655-3

10.1002/9781118762547

Hosseini‐Nasab M, 2013, Cross‐validation approximation in functional linear regression, JSCS, 83, 1429

10.1016/j.neuroimage.2013.06.020

HuangL. ScheiplF. GoldsmithJ. GellarJ. HarezlakJ. McLeanM. W. SwihartB. XiaoL. CrainiceanuC.&ReissP. (2015).refund: regression with functional data. R package version 0.1‐13.

HuoL. ReissP.&ZhaoY. (2014).refund.wave: wavelet‐domain regression with functional data. R package version 0.1.

10.1111/1467-9868.00342

10.1198/016214504000001556

10.1214/08-AOS641

10.1016/0022-247X(71)90184-3

10.2307/1913643

10.1016/j.jmva.2011.08.005

10.1080/01621459.2013.856794

10.1080/01621459.2013.788980

10.1080/10485252.2010.500385

Lian H, 2013, Shrinkage estimation and selection for multiple functional regression, Stat. Sin., 23, 51

10.1198/jasa.2009.tm08496

10.1080/01621459.2012.695640

10.1023/A:1008929526011

10.1093/biostatistics/kxq003

10.1002/bimj.201300072

10.1080/00401706.1999.10485591

10.1198/004017004000000626

McKeague I. W., 2014, Estimation of treatment policies based on functional predictors, Stat. Sin., 24, 1461

10.1214/10-AOS791

10.1007/s11222-014-9473-1

10.1080/10618600.2012.729985

10.1146/annurev-statistics-010814-020413

10.1214/009053604000001156

10.1093/biomet/ast004

10.1198/016214508000000751

10.1093/biomet/asq056

10.1137/1109020

10.1007/978-1-4612-0709-2

10.1016/j.jspi.2006.06.011

10.1016/j.csda.2003.10.003

10.1016/j.chemosphere.2010.11.025

R Core Team, 2015, R: a language and environment for statistical computing

10.1016/j.jspi.2006.10.001

10.1007/978-0-387-98185-7

10.1002/0470013192.bsa239

10.1214/12-EJS676

10.1002/sim.1067

10.1016/j.spl.2015.07.037

10.2202/1557-4679.1246

10.1214/15-AOAS829

10.1198/016214507000000527

10.1111/j.1467-9868.2008.00695.x

10.1111/j.1541-0420.2009.01233.x

10.1111/j.2517-6161.1991.tb01821.x

10.1017/CBO9780511755453

SchölkopfB. HerbrichR.&SmolaA. J. (2001.A generalized representer theorem.

Schölkopf B., 2002, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond.

10.1016/j.csda.2013.05.006

10.1080/10485252.2014.916806

10.1007/s00180-013-0463-0

10.1016/j.jmva.2015.06.015

10.1016/j.jspi.2009.03.001

10.1214/aos/1033066196

10.2307/1914309

10.1080/00401706.2013.863163

Laan M. J., 2007, Super learner, Stat. Appl. Genet. Molec. Biol., 6, Article 25

10.1137/1.9781611970128

WangJ.‐L. ChiouJ.‐M.&MüllerH.‐G. (2015).Review of functional data analysis. arXiv preprint arXiv:1507.05135.

10.1214/14-AOAS736

Watson G. S, 1964, Smooth regression analysis, Sankhya A, 26, 359

10.1016/S0893-6080(05)80023-1

10.1201/9781420010404

10.1111/j.1467-9868.2010.00749.x

10.1093/biomet/ass048

10.1007/s13253-013-0142-1

10.1093/biostatistics/kxq067

10.1198/016214504000001745

10.1093/biomet/asp069

10.1016/j.csda.2013.09.007

10.1016/j.csda.2014.04.016

10.1080/10618600.2014.925458

10.1080/10618600.2012.679241

10.1111/rssb.12031

10.1080/01621459.2013.776499

10.1111/j.1541-0420.2009.01283.x

10.1111/rssb.12036