242
Views
0
CrossRef citations to date
0
Altmetric
Articles

Robust scalar-on-function partial quantile regression

ORCID Icon, ORCID Icon & ORCID Icon
Pages 1359-1377 | Received 16 Dec 2022, Accepted 08 Apr 2023, Published online: 19 Apr 2023

References

  • J. Adrover, R.A. Maronna, and V.J. Yohai, Robust regression quantiles, J. Stat. Plan. Inference. 122 (2004), pp. 187–202.
  • A.M. Aguilera, M. Aguilera-Morillo, and C. Preda, Penalized versions of functional PLS regression, Chemometr. Intell. Lab. Syst. 154 (2016), pp. 8–92.
  • A.M. Aguilera, M. Escabias, C. Preda, and G. Saporta, Using basis expansions for estimating functional PLS regression applications with chemometric data, Chemometr. Intell. Lab. Syst. 104 (2010), pp. 289–305.
  • U. Beyaztas and H.L. Shang, Function-on-function linear quantile regression, Math. Modell. Anal. 27 (2022), pp. 322–341.
  • U. Beyaztas and H.L. Shang, A robust functional partial least squares for scalar-on-multiple-function regression, J. Chemom. 36 (2022), p. e3394.
  • U. Beyaztas, H.L. Shang, and A. Alin, Function-on-function partial quantile regression, J. Agricultural, Biol. Environmental Statist. 27 (2022), pp. 149–174.
  • C. Capezza, A. Lepore, A. Menafoglio, B. Palumbo, and S. Vantini, Control charts for monitoring ship operating conditions and CO2 emissions based on scalar-on-function regression, Appl. Stoch. Models. Bus. Ind. 36 (2020), pp. 477–500.
  • H. Cardot, C. Crambes, and P. Sarda, Quantile regression when the covariates are functions, J. Nonparametr. Stat. 17 (2005), pp. 841–856.
  • H. Cardot, C. Crambes, and P. Sarda, Ozone pollution forecasting using conditional mean and conditional quantiles with functional covariates, in Statistical Methods for Biostatistics and Related Fields, W. Hardle, Y. Mori, and P. Vieu, eds., Springer, Berlin, 2007, pp. 221–243.
  • M. Chaouch, A.A. Bouchentouf, A. Traore, and A. Rabhi, Single functional index quantile regression under general dependence structure, J. Nonparametr. Stat. 32 (2020), pp. 725–755.
  • K. Chen and H.G. Müller, Conditional quantile analysis when covariates are functions, with application to growth data, J. Royal Statist. Soc.: Ser. B 74 (2012), pp. 67–89.
  • J.E. Choi and D.W. Shin, Quantile correlation coefficient: a new tail dependence measure, Statist. Papers 63 (2022), pp. 1075–1104.
  • C. Crambes, A. Gannoun, and Y. Henchiri, Weak consistency of the support vector machine quantile regression approach when covariates are functions, Statist. Probab. Lett. 81 (2011), pp. 1847–1858.
  • C. Crambes, A. Gannoun, and Y. Henchiri, Support vector machine quantile regression approach for functional data: simulation and application studies, J. Multivar. Anal. 121 (2013), pp. 50–68.
  • A. Cuevas, A partial overview of the theory of statistics with functional data, J. Stat. Plan. Inference. 147 (2014), pp. 1–23.
  • Y. Dodge and J. Whittaker, Partial quantile regression, Metrika 70 (2009), pp. 35–57.
  • J.J. Dziak, D.L. Coffman, M. Reimherr, J. Petrovich, R. Li, S. Shiffman, and M.P. Shiyko, Scalar-on-function regression for predicting distal outcomes from intensively gathered longitudinal data: interpretability for applied scientists, Statist. Survey 36 (2019), pp. 150–180.
  • F. Ferraty, A. Rabhi, and P. Vieu, Conditional quantiles for dependent functional data with application to the climatic El Niño phenomenon, Sankhya: Indian J. Statist. 67 (2005), pp. 378–398.
  • F. Ferraty and P. Vieu, Nonparametric Functional Data Analysis, Springer, New York, 2006.
  • J. Goldsmith, J. Bobb, C.M. Crainiceanu, B. Caffo, and D. Reich, Penalized functional regression, J. Comput. Graph. Stat. 20 (2011), pp. 830–851.
  • J. Goldsmith, F. Scheipl, L. Huang, J. Wrobel, C. Di, J. Gellar, J. Harezlak, M.W. McLean, B. Swihart, L. Xiao, C. Crainiceanu, and P.T. Reiss, Refund: regression with functional data, R package version 0.1-22, 2020. Available at https://CRAN.R-project.org/package=refund.
  • S. Greven, C.M. Crainiceanu, and D. Reich, Longitudinal functional principal component analysis, Electron. J. Stat. 4 (2010), pp. 1022–1054.
  • S. Greven and F. Scheipl, A general framework for functional regression modelling, Stat. Modell. 17 (2017), pp. 1–35.
  • D.M.A. Gronwall, Paced auditory serial-addition task: a measure of recovery from concussion, Percept. Mot. Skills. 44 (1977), pp. 367–373.
  • L. Hao and D.Q. Naiman, Quantile Regression, Sage Publications, California, 2007.
  • L. Horvath and P. Kokoszka, Inference for Functional Data with Applications, Springer, New York, 2012.
  • T. Hsing and R. Eubank, Theoretical Foundations of Functional Data Analysis, with An Introduction to Linear Operators, John Wiley & Sons, Chennai, India, 2015.
  • A.E. Ivanescu, A.M. Staicu, F. Scheipl, and S. Greven, Penalized function-on-function regression, Comput. Stat. 30 (2015), pp. 539–568.
  • K. Kato, Estimation in functional linear quantile regression, Ann. Statist. 40 (2012), pp. 3108–3136.
  • R. Koenker, Quantile Regression, Cambridge University Press, New York, 2005.
  • P. Kokoszka and M. Reimherr, Introduction to Functional Data Analysis, CRC Press, Boca Raton, 2017.
  • G. Li, Y. Li, and C.L. Tsai, Quantile correlations and quantile autoregressive modeling, J. Amer. Statist. Assoc.: Theory Methods 110 (2015), pp. 246–261.
  • M. Li, K. Wang, A. Maity, and A.M. Staicu, Inference in functional linear quantile regression, J. Multivar. Anal. 190 (2022), p. 104985.
  • H. Ma, T. Li, H. Zhu, and Z. Zhu, Quantile regression for functional partially linear model in ultra-high dimensions, Comput. Statist. Data Anal. 129 (2019), pp. 135–147.
  • J.A. Matias-Guiu, A. Cortes-Martinez, P. Montero, V. Pytel, T. Moreno-Ramos, M. Jorquera, M. Yus, J. Arrazola, and J. Matias-Guiu, Structural mri correlates of pasat performance in multiple sclerosis, BMC. Neurol. 18 (2018), p. 214.
  • M.W. McLean, G. Hooker, A.M. Staicu, F. Scheipl, and D. Ruppert, Functional generalized additive models, J. Comput. Graph. Stat. 23 (2014), pp. 249–269.
  • A. Mendez-Civieta, M.C. Aguilera-Morillo, and R.E. Lillo, Fast partial quantile regression, Chemometr. Intell. Lab. Syst. 223 (2020), p. 104533.
  • S. Ozakbas, B.P. Cinar, M.A. Gurkan, O. Ozturk, D. Oz, and B.B. Kursun, Paced auditory serial addition test: national normative data, Clin. Neurol. Neurosurg. 140 (2016), pp. 97–99.
  • A. Ozturk, S.A. Smith, E.M. Gordon-Lipkin, D.M. Harrison, N. Shiee, D.L. Pham, B.S. Caffo, P.A. Calabresi, and D.S. Reich, Mri of the corpus callosum in multiple sclerosis: association with disability, Multiple Sclerosis 16 (2010), pp. 166–177.
  • C. Preda and G. Saporta, PLS regression on a stochastic process, Comput. Stat. Data. Anal. 48 (2005), pp. 149–158.
  • J.O. Ramsay and B.W. Silverman, Functional Data Analysis, Springer, New York, 2006.
  • P.T. Reiss, J. Goldsmith, H.L. Shang, and R.T. Odgen, Methods for scalar-on-function regression, Int. Statist. Rev. 85 (2017), pp. 228–249.
  • M. Rodriguez, A. Siva, J. Ward, K. Stolp-Smith, P. O'Brien, and L. Kurland, Impairment, disability, and handicap in multiple sclerosis: a population-based study in Olmsted County, Minnesota, Neurology 44 (1994), pp. 28–33.
  • P. Sang and J. Cao, Functional single-index quantile regression models, Stat. Comput. 30 (2020), pp. 771–781.
  • S. Serneels, C. Croux, P. Filzmoser, and P.J.V. Espen, Partial robust M-regression, Chemometr. Intell. Lab. Syst. 79 (2005), pp. 55–64.
  • A.M. Staicu, C.M. Crainiceanu, D.S. Reich, and D. Ruppert, Modeling functional data with spatially heterogeneous shape characteristics, Biometrics 68 (2012), pp. 331–343.
  • Y. Sun and M.G. Genton, Functional boxplots, J. Comput. Graph. Stat. 20 (2011), pp. 316–334.
  • B.J. Swihart, J. Goldsmith, and C.M. Crainiceanu, Restricted likelihood ratio test for functional effects in the functional linear model, Technometrics 56 (2014), pp. 483–493.
  • Q. Tang and L. Cheng, Partial functional linear quantile regression, Sci. China Math. 57 (2014), pp. 2589–2608.
  • F. Yao, S. Sue-Chee, and F. Wang, Regularized partially functional quantile regression, J. Multivar. Anal. 156 (2017), pp. 39–56.
  • D. Yu, L. Kong, and I. Mizera, Partial functional linear quantile regression for neuroimaging data analysis, Neurocomputing 195 (2016), pp. 74–87.
  • Z. Zhou, Fast implementation of partial least squares for function-on-function regression, J. Multivar. Anal. 185 (2021), p. 104769.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.