Asymptotic normality of the local linear estimator of the functional expectile regression

O Litimein, A Laksaci, L Ait-Hennani, B Mechab… - Journal of Multivariate …, 2024 - Elsevier
O Litimein, A Laksaci, L Ait-Hennani, B Mechab, M Rachdi
Journal of Multivariate Analysis, 2024Elsevier
We are concerned with the nonparametric estimation of the expectile functional regression.
More precisely, we build an estimator, by the local linear smoothing approach, of the
conditional expectile. Then we establish the asymptotic distribution of the constructed
estimator. Establishing this result requires the Bahadur representation of the conditional
expectile. The latter is obtained under certain standard conditions which cover the functional
aspect of the data as well as the nonparametric characteristic of the model. The real impact …
Abstract
We are concerned with the nonparametric estimation of the expectile functional regression. More precisely, we build an estimator, by the local linear smoothing approach, of the conditional expectile. Then we establish the asymptotic distribution of the constructed estimator. Establishing this result requires the Bahadur representation of the conditional expectile. The latter is obtained under certain standard conditions which cover the functional aspect of the data as well as the nonparametric characteristic of the model. The real impact of this result in nonparametric functional statistics has been discussed and highlighted using artificial data.
Elsevier
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