{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:12:34Z","timestamp":1760145154828,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T00:00:00Z","timestamp":1719705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2024R515","R.G.P. 1\/128\/45"],"award-info":[{"award-number":["PNURSP2024R515","R.G.P. 1\/128\/45"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]},{"name":"King Khalid University","award":["PNURSP2024R515","R.G.P. 1\/128\/45"],"award-info":[{"award-number":["PNURSP2024R515","R.G.P. 1\/128\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/axioms13070444","type":"journal-article","created":{"date-parts":[[2024,7,1]],"date-time":"2024-07-01T10:14:46Z","timestamp":1719828886000},"page":"444","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Strong Consistency of Incomplete Functional Percentile Regression"],"prefix":"10.3390","volume":"13","author":[{"given":"Mohammed B.","family":"Alamari","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9198-4903","authenticated-orcid":false,"given":"Fatimah A.","family":"Almulhim","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ouahiba","family":"Litimein","sequence":"additional","affiliation":[{"name":"Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Boubaker","family":"Mechab","sequence":"additional","affiliation":[{"name":"Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, Sidi Bel Abbes 22000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0167-7152(89)90095-3","article-title":"Nonparametric estimation of conditional quantiles","volume":"7","author":"Samanta","year":"1989","journal-title":"Statist. Probab. 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