The functional kNN estimator of the conditional expectile: Uniform consistency in number of neighbors

Almanjahie Ibrahim M. (), Bouzebda Salim (), Chikr Elmezouar Zouaoui () and Laksaci Ali ()
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Almanjahie Ibrahim M.: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, 61413 Abha, Saudi Arabia
Bouzebda Salim: Alliance Sorbonne Universités, Université de Technologie de Compiègne, Laboratoire de Mathématiques Appliquées de Compiègne, Compiègne, France
Chikr Elmezouar Zouaoui: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, 61413 Abha, Saudi Arabia
Laksaci Ali: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, 61413 Abha, Saudi Arabia

Statistics & Risk Modeling, 2021, vol. 38, issue 3-4, 47-63

Abstract: The main purpose of the present paper is to investigate the problem of the nonparametric estimation of the expectile regression in which the response variable is scalar while the covariate is a random function. More precisely, an estimator is constructed by using the k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors (UNN) of the constructed estimator. The usefulness of our result for the smoothing parameter automatic selection is discussed. Short simulation results show that the finite sample performance of the proposed estimator is satisfactory in moderate sample sizes. We finally examine the implementation of this model in practice with a real data in financial risk analysis.

Keywords: Functional data analysis; expectile regression; UNN consistency; functional nonparametric statistics; almost complete convergence rate (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1515/strm-2019-0029

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