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On dimension reduction models for functional data

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  • Vieu, Philippe

Abstract

This contribution is part of the recent links between Functional Data and Big Data communities. A selected survey highlights how earlier ideas in high dimensional problems can be adapted in functional setting.

Suggested Citation

  • Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    • Handle: RePEc:eee:stapro:v:136:y:2018:i:c:p:134-138
    DOI: 10.1016/j.spl.2018.02.032
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    References listed on IDEAS

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    1. Berrendero, José R. & Cuevas, Antonio & Pateiro-López, Beatriz, 2016. "Shape classification based on interpoint distance distributions," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 237-247.
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    3. Germán Aneiros & Philippe Vieu, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 27-32, March.
    4. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 231-255, September.
    5. Shujie Ma, 2016. "Estimation and inference in functional single-index models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 181-208, February.
    6. Fraiman, Ricardo & Gimenez, Yanina & Svarc, Marcela, 2016. "Feature selection for functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 191-208.
    7. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    8. Collazos, Julian A.A. & Dias, Ronaldo & Zambom, Adriano Z., 2016. "Consistent variable selection for functional regression models," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 63-71.
    9. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
    10. Kara, Lydia-Zaitri & Laksaci, Ali & Rachdi, Mustapha & Vieu, Philippe, 2017. "Data-driven kNN estimation in nonparametric functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 176-188.
    11. Aneiros, Germán & Vieu, Philippe, 2014. "Variable selection in infinite-dimensional problems," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 12-20.
    12. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    13. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    14. Lydia Kara-Zaitri & Ali Laksaci & Mustapha Rachdi & Philippe Vieu, 2017. "Uniform in bandwidth consistency for various kernel estimators involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 85-107, January.
    15. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
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    17. Boente, Graciela & Vahnovan, Alejandra, 2017. "Robust estimators in semi-functional partial linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 59-84.
    18. Floriello, Davide & Vitelli, Valeria, 2017. "Sparse clustering of functional data," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 1-18.
    19. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    20. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    21. Laura M. Sangalli & James O. Ramsay & Timothy O. Ramsay, 2013. "Spatial spline regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 681-703, September.
    22. Hans-Georg Müller & Yichao Wu & Fang Yao, 2013. "Continuously additive models for nonlinear functional regression," Biometrika, Biometrika Trust, vol. 100(3), pages 607-622.
    23. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    24. Demongeot, Jacques & Naceri, Amina & Laksaci, Ali & Rachdi, Mustapha, 2017. "Local linear regression modelization when all variables are curves," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 37-44.
    25. Kokoszka, Piotr & Oja, Hanny & Park, Byeong & Sangalli, Laura, 2017. "Special issue on functional data analysis," Econometrics and Statistics, Elsevier, vol. 1(C), pages 99-100.
    26. Germán Aneiros & Philippe Vieu, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 27-32, March.
    27. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.
    28. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
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    Citations

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    Cited by:

    1. Sultana Didi & Salim Bouzebda, 2022. "Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes," Mathematics, MDPI, vol. 10(22), pages 1-37, November.
    2. Reid, Nancy, 2018. "Statistical science in the world of big data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 42-45.
    3. Shuyu Meng & Zhensheng Huang, 2024. "Variable Selection in Semi-Functional Partially Linear Regression Models with Time Series Data," Mathematics, MDPI, vol. 12(17), pages 1-23, September.
    4. Aneiros, Germán & Novo, Silvia & Vieu, Philippe, 2022. "Variable selection in functional regression models: A review," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    6. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    8. Bodnar, Taras & Okhrin, Ostap & Parolya, Nestor, 2019. "Optimal shrinkage estimator for high-dimensional mean vector," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 63-79.
    9. Sultana DIDI & Ahoud AL HARBY & Salim BOUZEBDA, 2022. "Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time," Mathematics, MDPI, vol. 10(19), pages 1-33, September.
    10. Torrecilla, José L. & Romo, Juan, 2018. "Data learning from big data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 15-19.
    11. Bouzebda, Salim & Chaouch, Mohamed, 2022. "Uniform limit theorems for a class of conditional Z-estimators when covariates are functions," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Novo, Silvia & Aneiros, Germán & Vieu, Philippe, 2021. "A kNN procedure in semiparametric functional data analysis," Statistics & Probability Letters, Elsevier, vol. 171(C).
    13. Silvia Novo & Germán Aneiros & Philippe Vieu, 2021. "Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 481-504, June.

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