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A Journal of Theoretical and Applied Statistics
Volume 42, 2008 - Issue 6
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Original Articles

Cross-validated estimations in the single-functional index model

Ahmed Ait-Saïdi Lab. de Mathématiques Appliquées, Université Abderahmane Mira, Route de Tergua Ouzemour, Béjaia, Algerie
,
Frédéric Ferraty Lab. de Statistique et Probabilités, Université Paul Sabatier, 118, route de Narbonne, Toulouse Cedex 4, FranceCorrespondence[email protected]
,
Rabah Kassa Lab. de Mathématiques Appliquées, Université Abderahmane Mira, Route de Tergua Ouzemour, Béjaia, Algerie
&
Philippe Vieu Lab. de Statistique et Probabilités, Université Paul Sabatier, 118, route de Narbonne, Toulouse Cedex 4, France
Pages 475-494 | Received 07 Dec 2006, Published online: 20 Oct 2008

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Shuyu Meng, Zhensheng Huang, Jing Zhang & Zhiqiang Jiang. (2023) Estimation on functional partially linear single index measurement error model. Communications in Statistics - Theory and Methods 52:13, pages 4741-4763.
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Piaoxuan Xiao & Guochang Wang. (2022) Partial functional linear regression with autoregressive errors. Communications in Statistics - Theory and Methods 51:13, pages 4515-4536.
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Tao Zhang, Haifeng Huo & Yanling Wan. (2021) Functional polynomial multiple-index model. Communications in Statistics - Simulation and Computation 50:12, pages 3958-3971.
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Han Lin Shang. (2020) Estimation of a functional single index model with dependent errors and unknown error density. Communications in Statistics - Simulation and Computation 49:12, pages 3111-3133.
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Mohamed Chaouch, Amina Angelika Bouchentouf, Aboubacar Traore & Abbes Rabhi. (2020) Single functional index quantile regression under general dependence structure. Journal of Nonparametric Statistics 32:3, pages 725-755.
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Tabti Hadjila & Ait Saidi Ahmed. (2018) Estimation and simulation of conditional hazard function in the quasi-associated framework when the observations are linked via a functional single-index structure. Communications in Statistics - Theory and Methods 47:4, pages 816-838.
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Ahmed Ait Saidi & Mecheri Kheira. (2016) The conditional cumulative distribution function in single functional index model. Communications in Statistics - Theory and Methods 45:16, pages 4896-4911.
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André Mas. (2012) Lower bound in regression for functional data by representation of small ball probabilities. Electronic Journal of Statistics 6:none.
Crossref
. 2011. Statistical Learning and Data Science. Statistical Learning and Data Science 205 212 .
Dong Chen, Peter Hall & Hans-Georg Müller. (2011) Single and multiple index functional regression models with nonparametric link. The Annals of Statistics 39:3.
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Qin Wang & Xiangrong Yin. (2011) Estimation of inverse mean: An orthogonal series approach. Computational Statistics & Data Analysis 55:4, pages 1656-1664.
Crossref
Gery Geenens. (2011) Curse of dimensionality and related issues in nonparametric functional regression. Statistics Surveys 5:none.
Crossref
Said Attaoui, Ali Laksaci & Elias Ould Said. (2011) A note on the conditional density estimate in the single functional index model. Statistics & Probability Letters 81:1, pages 45-53.
Crossref
Frédéric Ferraty, Adela Martínez-Calvo & Philippe Vieu. 2011. Recent Advances in Functional Data Analysis and Related Topics. Recent Advances in Functional Data Analysis and Related Topics 103 109 .
Laurent Delsol, Frédéric Ferraty & Philippe Vieu. 2011. Recent Advances in Functional Data Analysis and Related Topics. Recent Advances in Functional Data Analysis and Related Topics 77 83 .
F. Ferraty, P. Hall & P. Vieu. (2010) Most-predictive design points for functional data predictors. Biometrika 97:4, pages 807-824.
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Xuerong Meggie Wen. (2010) On sufficient dimension reduction for proportional censorship model with covariates. Computational Statistics & Data Analysis 54:8, pages 1975-1982.
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Laurent Delsol. (2008) Tests de structure en régression sur variable fonctionnelle. Comptes Rendus. Mathématique 346:5-6, pages 343-346.
Crossref
Sophie Dabo-Niang & Frédéric FerratyLaurent Delsol. 2008. Functional and Operatorial Statistics. Functional and Operatorial Statistics 143 150 .

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