Smooth k NN Local Linear Estimation of the Conditional Distribution Function

Ibrahim M. Almanjahie, Zouaoui Chikr Elmezouar, Ali Laksaci and Mustapha Rachdi
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Ibrahim M. Almanjahie: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Zouaoui Chikr Elmezouar: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Ali Laksaci: Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
Mustapha Rachdi: AGIM Team, Laboratoire AGEIS, EA 7407, Université Grenoble Alpes (France), UFR SHS, BP. 47, CEDEX 09, F38040 Grenoble, France

Mathematics, 2021, vol. 9, issue 10, 1-14

Abstract: Previous works were dedicated to the functional k -Nearest Neighbors ( k NN) and the local linearity method estimations of a regression operator. In this paper, a sequence pair of ( X i , Y i ) i = 1 , … , n of functional mixing observations are considered. We treat the local linear estimation of the cumulative function of Y i given functional input variable X i . Precisely, we combine the k NN method with the local linear algorithm to construct a new and fast efficiency estimator of the conditional distribution function. The main purpose of this paper is to prove the strong convergence of the constructed estimator under mixing conditions. An application to the functional times series prediction is used to compare our proposed estimator with the existing competitive estimators, and show its efficiency and superiority.

Keywords: functional mixing data; complete convergence (a.co.); Local Linear Fitting (LLM); distribution function; kernel weighting; conditional predictive region; k nearest neighbors smoothing ( k NN) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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