{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:18:50Z","timestamp":1753885130329,"version":"3.41.2"},"reference-count":35,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"Open Foundation of Hubei Key Laboratory of Applied Mathematics","award":["HBAM202203."],"award-info":[{"award-number":["HBAM202203."]}]},{"name":"Hubei Education Science Planning Project","award":["2020GB198"],"award-info":[{"award-number":["2020GB198"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:p>Partially linear additive models (PLAMs) have attracted much attention in the statistical machine learning community due to their interpretability and flexibility in data-driven prediction and inference. Since the performance of PLAMs is closely related to the structure information of linear and nonlinear components, several approaches have been proposed for regression estimation and data-driven structure discovery. However, the existing automatic discovery strategy is limited to the mean regression framework and is usually sensitive to non-Gaussian noises, e.g. skewed noise and heavy-tailed noise. To further improve the robustness of PLAMs, this paper proposes a Robust Partially Linear Trend Filtering (RPLTF) for regression estimation and structure discovery by integrating the mode-induced error metric and the trend filtering-based nonlinear approximation into regularized PLAMs. Besides the computing algorithm of RPLTF, we establish its upper bound on generalization error in theory. Empirical examples are provided to validate the effectiveness of the proposed\u00a0method.<\/jats:p>","DOI":"10.1142\/s021969132350039x","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T16:19:21Z","timestamp":1690561161000},"source":"Crossref","is-referenced-by-count":0,"title":["Robust partially linear trend filtering for regression estimation and structure discovery"],"prefix":"10.1142","volume":"22","author":[{"given":"Hao","family":"Deng","sequence":"first","affiliation":[{"name":"College of Informatics, Huazhong Agricultural University, Wuhan 430070, P. R. China"},{"name":"Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, P. R. China"}]},{"given":"Yuxiang","family":"Han","sequence":"additional","affiliation":[{"name":"College of Informatics, Huazhong Agricultural University, Wuhan 430070, P. R. 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