Rate of the almost sure convergence of a generalized regression estimate based on truncated and functional data
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 480-491.

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In this paper, a nonparametric estimation of a generalized regression function is proposed. The real response random variable (r.v.) is subject to left-truncation by another r.v. while the covariate takes its values in an infinite dimensional space. Under standard assumptions, the pointwise and the uniform almost sure convergences, of the proposed estimator, are established.
Keywords: functional data, truncated data, almost sure convergence, local linear estimator.
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Halima Boudada; Sara Leulmi; Soumia Kharfouch. Rate of the almost sure convergence of a generalized regression estimate based on truncated and functional data. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 4, pp. 480-491. http://geodesic.mathdoc.fr/item/JSFU_2020_13_4_a9/

[1] J. Barrientos-Marin, F. Ferraty, P. Vieu, Journal of Nonparametric Statistics, 22:5 (2010), 617–632 | DOI

[2] S. Derrar, A. Laksaci, E. Ould Sa\"{i}d, Journal of Statistical Theory and Practice, 9:4 (2015), 823–849 | DOI

[3] F. Ferraty, P. Vieu, Nonparametric functional data analysis: theory and practice, Springer Science Business Media, 2006

[4] S. He, G.L. Yang, Estimation of the truncation probability in the random truncation model, 1998, 1011–1027

[5] N. Helal, E. Ould-Sa\"{i}d, Kernel conditional quantile estimator under left truncation for functional regressors, 36 (2016), 25–48

[6] M. Lemdani, E. Ould-Said, Asymptotic behavior of the hazard rate kernel estimator under truncated and censored data, 36:1 (2007), 155–173

[7] S. Leulmi, F. Messaci, Journal of Siberian Federal University. Mathematics abd Physics, 12 (2019), 379–391 | DOI

[8] S. Leulmi, F. Messaci, “Local linear estimation of a generalized regression function with functional dependent data”, Communications in Statistics – Theory and Methods, 47:23 (2018), 5795–5811

[9] F. Messaci, N. Nemouchi, I. Ouassou, M. Rachdi, Statistical Methods $\$ Applications, 24:4 (2015), 597–622 | DOI

[10] W. Stute, “Almost sure representations of the product-limit estimator for truncated data”, The Annals of Statistics, 21:1 (1993), 146–156

[11] M. Woodroofe, “Estimating a distribution function with truncated data”, The Annals of Statistics, 13:1 (1985), 163–177

[12] X. Xiong, P. Zhou, C. Ailian, “Asymptotic normality of the local linear estimation of the conditional density for functional time-series data”, Communications in Statistics – Theory and Methods, 47:14 (2018), 3418–3440