{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:59:27Z","timestamp":1760057967700,"version":"build-2065373602"},"reference-count":128,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T00:00:00Z","timestamp":1741132800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we examine a class of partially linear additive models (PLAM) defined via a measurable mapping \u03a8:Rq\u2192R. More precisely, we consider \u03a8(Yi):=Yi=Zi\u22a4\u03b2+\u2211l=1dml(Xl,i)+\u03b5i,i=1,\u2026,n, where Zi=(Zi,1,\u2026,Zi,p)\u22a4 and Xi=(X1,i,\u2026,Xd,i)\u22a4 denote vectors of explanatory variables. The unknown parameter vector is \u03b2=(\u03b21,\u2026,\u03b2p)\u22a4, and m1,\u2026,md are real-valued functions of a single variable whose forms are not specified. The error terms \u03b51,\u2026,\u03b5n are identically distributed with mean zero and finite variance \u03c3\u03b5, and they fulfill the condition E(\u03b5\u2223X,Z)=0 almost surely. These models are broadly applicable in finance, biology, and engineering, where capturing intricate nonlinear effects is essential. We propose an estimation method that leverages marginal integration in conjunction with linear wavelet-based techniques to obtain estimators for the unknown components m1,\u2026,md. Under suitable regularity conditions, we establish strong uniform convergence of these estimators, demonstrating that they achieve practically relevant convergence rates. Our theoretical results indicate that these estimators converge uniformly at rates that are favorable for practical applications, underscoring the adaptability and scope of this partially linear additive model.<\/jats:p>","DOI":"10.3390\/sym17030394","type":"journal-article","created":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T09:37:52Z","timestamp":1741167472000},"page":"394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Almost Sure Rate of Convergence for the Wavelets Estimator in the Partially Linear Additive Models"],"prefix":"10.3390","volume":"17","author":[{"given":"Khalid","family":"Chokri","sequence":"first","affiliation":[{"name":"Modeling and Complex Systems Laboratory-M.C.S.L., Cadi Ayyad University, P.B. 549, Marrakech 40001, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7801-4945","authenticated-orcid":false,"given":"Salim","family":"Bouzebda","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques Appliqu\u00e9es de Compi\u00e8gne-L.M.A.C., Universit\u00e9 de Technologie de Compi\u00e8gne, 60205 Compi\u00e8gne Cedex, France"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2247","DOI":"10.1214\/21-EJS1820","article-title":"A penalized likelihood approach for efficiently estimating a partially linear additive transformation model with current status data","volume":"15","author":"Liu","year":"2021","journal-title":"Electron. 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