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Open AccessArticle
Strong Consistency of Incomplete Functional Percentile Regression
by
Mohammed B. Alamari
Mohammed B. Alamari 1,
Fatimah A. Almulhim
Fatimah A. Almulhim 2,*
,
Ouahiba Litimein
Ouahiba Litimein 3 and
Boubaker Mechab
Boubaker Mechab 3
1
Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
2
Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3
Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, Algeria
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(7), 444; https://doi.org/10.3390/axioms13070444 (registering DOI)
Submission received: 24 May 2024
/
Revised: 18 June 2024
/
Accepted: 22 June 2024
/
Published: 30 June 2024
Abstract
This paper analyzes the co-fluctuation between a scalar response random variable and a curve regressor using quantile regression. We focus on the situation wherein the output variable is observed with random missing. For this incomplete functional data situation, we estimate the quantile regression by combining two principal nonparametric methods: the local linearity approach (LLA) and the kernel nearest neighbor (KNN) algorithm. We study the asymptotic properties of the constructed estimator by establishing, under general assumptions, uniform consistency over the number of neighborhoods. This asymptotic result provides good mathematical support for the selection of the optimal neighborhood. We examine the feasibility of the constructed estimator using artificially generated data. Moreover, we apply the quantile regression technique in food quality by predicting the riboflavin quantity in yogurt using spectrometry data.
Share and Cite
MDPI and ACS Style
Alamari, M.B.; Almulhim, F.A.; Litimein, O.; Mechab, B.
Strong Consistency of Incomplete Functional Percentile Regression. Axioms 2024, 13, 444.
https://doi.org/10.3390/axioms13070444
AMA Style
Alamari MB, Almulhim FA, Litimein O, Mechab B.
Strong Consistency of Incomplete Functional Percentile Regression. Axioms. 2024; 13(7):444.
https://doi.org/10.3390/axioms13070444
Chicago/Turabian Style
Alamari, Mohammed B., Fatimah A. Almulhim, Ouahiba Litimein, and Boubaker Mechab.
2024. "Strong Consistency of Incomplete Functional Percentile Regression" Axioms 13, no. 7: 444.
https://doi.org/10.3390/axioms13070444
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