Geodesic
Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates
Kybernetika, Tome 57 (2021) no. 5, pp. 819-839.

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In this paper, we investigate the problem of the conditional cumulative of a scalar response variable given a random variable taking values in a semi-metric space. The uniform almost complete consistency of this estimate is stated under some conditions. Moreover, as an application, we use the obtained results to derive some asymptotic properties for the local linear estimator of the conditional quantile.
DOI : 10.14736/kyb-2021-5-0819
Classification : 62G08, 62G20
Keywords: functional data; local linear estimator; conditional cumulative; conditional quantile; nonparametric regression; small balls probability 
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     title = {Local linear estimation of conditional cumulative distribution function in the functional data: {Uniform} consistency with convergence rates},
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Hebchi, Chaima; Chouaf, Abdelhak. Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates. Kybernetika, Tome 57 (2021) no. 5, pp. 819-839. doi : 10.14736/kyb-2021-5-0819. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2021-5-0819/

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