Kybernetika 57 no. 5, 819-839, 2021

Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates

Chaima Hebchi and Abdelhak ChouafDOI: 10.14736/kyb-2021-5-0819

Abstract:

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.

Keywords:

nonparametric regression, functional data, local linear estimator, conditional cumulative, conditional quantile, small balls probability

Classification:

62G08, 62G20

paper.pdf

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