Asymptotic Results of a Recursive Double Kernel Estimator of the Conditional Quantile for Functional Ergodic Data
by Imane Bouazza   Fatima Benziadi   Fethi Madani   Toufik Guendouzi  

Vol. 16 No. 3 (2021) P.217~P.239

DOI:	https://doi.org/10.21915/BIMAS.2021302
	10.21915/BIMAS.2021302

ABSTRACT

The aim of our paper is to investigate the estimation of conditional quantile of a scalar response variable $Y$ given a random variable (rv) $X = x$ taking values in a semimetric space. Hence, the asymptotic normality of the proposed estimator is obtained when the observations are sampled from a functional ergodic process. The result confirms the prospect proposed in Benziadi et al. [3] and as applications, a comparison study based on a finite-sample behavior of the estimator is investigated by simulations as well.

KEYWORDS
Asymptotic normality, Conditional quantile, Recursive estimate, Ergodic data, Functional data, Small ball probability.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 62G20, 62G08, 62G35, 62E20

MILESTONES

Received: 2021-07-24
Revised :
Accepted: 2021-09-28

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