{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:42:03Z","timestamp":1760060523958,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T00:00:00Z","timestamp":1756425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation (NSF) project of Shandong Province of China","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}]},{"name":"Ministry of education of Humanities and Social Science project","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"],"award-info":[{"award-number":["2021YFA1000102","ZR2024MA074","24YJA910003","23CX03012A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We present the first differentially private framework for stochastic frontier analysis (SFA), addressing the challenge of non-convex objectives in privacy-preserving efficiency estimation. We construct a bounded parameter space to control gradient sensitivity and adapt the Frank\u2013Wolfe algorithm with calibrated linear oracle noise to mitigate cumulative perturbation. Incorporating l1-regularization facilitates sparse and interpretable variable selection under strict (\u03f5,\u03b4)-differential privacy. Experiments demonstrate 15\u201335% MAE reduction under \u03f5=0.1, along with strong scalability and estimation accuracy compared to prior DP methods for non-convex models.<\/jats:p>","DOI":"10.3390\/axioms14090667","type":"journal-article","created":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T16:42:21Z","timestamp":1756485741000},"page":"667","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Privacy-Preserving Statistical Inference for Stochastic Frontier Analysis"],"prefix":"10.3390","volume":"14","author":[{"given":"Mengxiang","family":"Quan","sequence":"first","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}]},{"given":"Yunquan","family":"Song","sequence":"additional","affiliation":[{"name":"College of Science, China University of Petroleum, Qingdao 266580, China"}]},{"given":"Xinmin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Economics and Management, China University of Petroleum, Qingdao 266580, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,29]]},"reference":[{"key":"ref_1","unstructured":"Kumbhakar, S.C., and Lovell, C.K. 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