{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:44:26Z","timestamp":1760060666855,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T00:00:00Z","timestamp":1757980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Provincial Natural Science Foundation of Hunan","award":["2023JJ30187","24A0518"],"award-info":[{"award-number":["2023JJ30187","24A0518"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["2023JJ30187","24A0518"],"award-info":[{"award-number":["2023JJ30187","24A0518"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, we propose a novel penalized empirical likelihood approach that simultaneously performs parameter estimation and variable selection in heteroscedastic partially linear single-index models with a diverging number of parameters. It is rigorously proved that the proposed method possesses the oracle property: (i) with probability tending to 1, the zero components are consistently estimated as zero; (ii) the estimators for nonzero coefficients achieve asymptotic efficiency. Furthermore, the penalized empirical log-likelihood ratio statistic is shown to asymptotically follow a standard chi-squared distribution under the null hypothesis. This methodology can be naturally applied to pure partially linear models and single-index models in high-dimensional settings. Simulation studies and real-world data analysis are conducted to examine the properties of the presented approach.<\/jats:p>","DOI":"10.3390\/e27090964","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T11:19:31Z","timestamp":1758021571000},"page":"964","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Statistical Inference for High-Dimensional Heteroscedastic Partially Single-Index Models"],"prefix":"10.3390","volume":"27","author":[{"given":"Jianglin","family":"Fang","sequence":"first","affiliation":[{"name":"College of Science, Hunan Institute of Engineering, Fuxing Road, Xiangtan 411104, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhikun","family":"Tian","sequence":"additional","affiliation":[{"name":"College of Science, Hunan Institute of Engineering, Fuxing Road, Xiangtan 411104, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1080\/01621459.1997.10474001","article-title":"Generalized partially linear single-index models","volume":"92","author":"Carroll","year":"1997","journal-title":"J. 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