The local linear functional kNN estimator of the conditional expectile: uniform consistency in number of neighbors

Ibrahim M. Almanjahie (), Salim Bouzebda (), Zoulikha Kaid () and Ali Laksaci ()
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Ibrahim M. Almanjahie: King Khalid University
Salim Bouzebda: Université de Technologie de Compiègne
Zoulikha Kaid: King Khalid University
Ali Laksaci: King Khalid University

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 8, No 4, 1007-1035

Abstract: 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 local linear k Nearest Neighbor procedures (kNN). The main contribution of this study is the establishment of the Uniform consistency in Number of Neighbors of the constructed estimators. These results are established under fairly general structural conditions on the classes of functions and the underlying models. The usefulness of our result for the smoothing parameter automatic selection is discussed. Some simulation studies are carried out to show the finite sample performances of the kNN estimator. The theoretical uniform consistency results, established in this paper, are (or will be) key tools for many further developments in functional data analysis.

Keywords: Functional data analysis; Expectile regression; kNN method; UNN consistency; Functional nonparametric statistics; Almost complete convergence rate; 62G05; 62G08; 62G20; Secondary 62H12 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00184-023-00942-0

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