{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T14:48:40Z","timestamp":1761058120654,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2025R358"],"award-info":[{"award-number":["PNURSP2025R358"]}]},{"name":"The Deanship of Research and Graduate Studies at King Khalid University","award":["R.G.P.1\/118\/46"],"award-info":[{"award-number":["R.G.P.1\/118\/46"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper examines the asymptotic behavior of the conditional hazard function using kernel-based methods, with particular emphasis on functional weakly dependent data. In particular, we establish the asymptotic normality of the proposed estimator when the covariate follows a functional quasi-associated process. This contribution extends the scope of nonparametric inference under weak dependence within the framework of functional data analysis. The estimator is constructed through kernel smoothing techniques inspired by the classical Nadaraya\u2013Watson approach, and its theoretical properties are rigorously derived under appropriate regularity conditions. To evaluate its practical performance, we carried out an extensive simulation study, where finite-sample outcomes were compared with their asymptotic counterparts. The results showed the robustness and reliability of the estimator across a range of scenarios, thereby confirming the validity of the proposed limit theorem in empirical settings.<\/jats:p>","DOI":"10.3390\/sym17101777","type":"journal-article","created":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T14:17:35Z","timestamp":1761056255000},"page":"1777","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Limit Theorem for Kernel Estimate of the Conditional Hazard Function with Weakly Dependent Functional Data"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1666-1044","authenticated-orcid":false,"given":"Abderrahmane","family":"Belguerna","sequence":"first","affiliation":[{"name":"Department of Mathematics, Science Institute, S.A University Center, P.O. Box 66, Naama 45000, Algeria"},{"name":"Laboratory of Mathematics, Statistics and Computer Science (W1550900), S.A University Center of Naama, Naama 45000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-5406-8883","authenticated-orcid":false,"given":"Abdelkader","family":"Rassoul","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Science Institute, S.A University Center, P.O. Box 66, Naama 45000, Algeria"},{"name":"Laboratory of Mathematics, Statistics and Computer Science (W1550900), S.A University Center of Naama, Naama 45000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5479-9346","authenticated-orcid":false,"given":"Hamza","family":"Daoudi","sequence":"additional","affiliation":[{"name":"Laboratory of Mathematics, Statistics and Computer Science (W1550900), S.A University Center of Naama, Naama 45000, Algeria"},{"name":"Department of Electrical Engineering, College of Technology, Tahri Mohamed University, Al-Qanadisa Road, P.O. Box 417, Bechar 08000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7621-6711","authenticated-orcid":false,"given":"Zouaoui Chikr","family":"Elmezouar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1306-7688","authenticated-orcid":false,"given":"Fatimah","family":"Alshahrani","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,21]]},"reference":[{"key":"ref_1","unstructured":"Bosq, D., and Lecoutre, J.B. (1987). Th\u00e9orie de L\u2019estimation Fonctionnelle, Economica."},{"key":"ref_2","unstructured":"Ferraty, F., and Vieu, P. (2006). Nonparametric Functional Data Analysis: Theory and Practice, Springer. 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