A class of local linear estimators with functional data
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 379-391.

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce a local linear nonparametric estimation for the generalized regression function of a scalar response variable given a random variable taking values in a semi metric space. We establish a rate of uniform consistency for the proposed estimators. Then, based on a real data set we illustrate the performance of a particular studied estimator with respect to other known estimators.
Keywords: locally modelled regression, nonparametric estimation, rate of convergence, uniform almost complete convergence.
@article{JSFU_2019_12_3_a12,
     author = {Sara Leulmi and Fatiha Messaci},
     title = {A class of local linear estimators with functional data},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {379--391},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a12/}
}
TY  - JOUR
AU  - Sara Leulmi
AU  - Fatiha Messaci
TI  - A class of local linear estimators with functional data
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2019
SP  - 379
EP  - 391
VL  - 12
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a12/
LA  - en
ID  - JSFU_2019_12_3_a12
ER  - 
%0 Journal Article
%A Sara Leulmi
%A Fatiha Messaci
%T A class of local linear estimators with functional data
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2019
%P 379-391
%V 12
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a12/
%G en
%F JSFU_2019_12_3_a12
Sara Leulmi; Fatiha Messaci. A class of local linear estimators with functional data. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 379-391. http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a12/

[1] J. Barrientos-Marin, F. Ferraty, P. Vieu, “Locally modelled regression and functional data”, J. of Nonparametric Statistics, 22 (2010), 617–632 | DOI | MR | Zbl

[2] K. Benhenni, F. Ferraty, M. Rachdi, P. Vieu, “Local smoothing regression with functional data”, Computational Statistics, 22:3 (2007), 353–369 | DOI | MR

[3] J. Demongeot, A. Laksaci, F. Madani, M. Rachdi, “Functional data analysis: conditional density estimation and its application”, Statistics, 47:1 (2013), 26–44 | DOI | MR | Zbl

[4] F. Ferraty, A. Laksaci, A. Tadj, P. Vieu, “Rate of uniform consistency for nonparametric estimates with functional variables”, Journal of Statistical planning and inference, 140 (2010), 335–352 | DOI | MR | Zbl

[5] F. Ferraty, I. Van Keilegom, P. Vieu, “On the validity of the bootstrap in nonparametric functional regression”, Scandinavian Journal of Statistics, 37:2 (2008), 286–306 | DOI | MR

[6] F. Ferraty, P. Vieu, Nonparametric functional data analysis. Theory and Practice, Springer Series in Statistics, New York, 2006 | MR | Zbl

[7] A.N. Kolmogorov, V.M. Tikhomirov, “$\varepsilon$-entropy and $\varepsilon$-capacity”, Uspekhi Matematicheskikh Nauk, 14 (1959), 3–86 (in Russian) | MR | Zbl

[8] F. Messaci, N. Nemouchi, I. Ouassou, M. Rachdi, “Local polynomial modelling of the conditional quantile for functional data”, Statistics Methods and Applications, 24:4 (2015), 597–622 | DOI | MR | Zbl