{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T16:35:59Z","timestamp":1785429359859,"version":"3.56.0"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:00:00Z","timestamp":1783468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"publisher","award":["2025AFC080"],"award-info":[{"award-number":["2025AFC080"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012554","name":"Hubei Provincial Department of Education","doi-asserted-by":"crossref","award":["D20243001"],"award-info":[{"award-number":["D20243001"]}],"id":[{"id":"10.13039\/100012554","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100012554","name":"Hubei Provincial Department of Education","doi-asserted-by":"crossref","award":["23Q166"],"award-info":[{"award-number":["23Q166"]}],"id":[{"id":"10.13039\/100012554","id-type":"DOI","asserted-by":"crossref"}]},{"award":["D20243001"],"award-info":[{"award-number":["D20243001"]}],"id":[{"id":"https:\/\/ror.org\/05yaa9j15","id-type":"ROR","asserted-by":"publisher"}]},{"award":["23Q166"],"award-info":[{"award-number":["23Q166"]}],"id":[{"id":"https:\/\/ror.org\/05yaa9j15","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012215","name":"Nanjing University of Finance and Economics","doi-asserted-by":"crossref","award":["XXCB3202404"],"award-info":[{"award-number":["XXCB3202404"]}],"id":[{"id":"10.13039\/501100012215","id-type":"DOI","asserted-by":"crossref"}]},{"award":["XXCB3202404"],"award-info":[{"award-number":["XXCB3202404"]}],"id":[{"id":"https:\/\/ror.org\/031y8am81","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Jiangsu Provincial Federation of Social Sciences Development Special Project","award":["25GSB-041"],"award-info":[{"award-number":["25GSB-041"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper focuses on a heteroscedastic partially linear regression model in which the errors are asymptotically almost negatively associated (AANA) random variables with a stochastically dominated and zero mean. Under some suitable conditions, the p-th p&gt;0 mean consistency of least squares estimators and weighted least squares estimators for the unknown parameter is established, and the p-th p&gt;0 mean consistency of the estimators for non-parametric components is also obtained. In addition, the moment convergence rate of the estimators is also investigated. Some results derived in this paper extend and improve the corresponding ones of negatively associated (NA) random errors and independent random errors. Finally, a simulation is carried out to study the numerical performance of the results that we have established.<\/jats:p>","DOI":"10.3390\/e28070776","type":"journal-article","created":{"date-parts":[[2026,7,9]],"date-time":"2026-07-09T14:17:51Z","timestamp":1783606671000},"page":"776","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mean Consistency of Estimators in a Partially Linear Model with AANA Errors"],"prefix":"10.3390","volume":"28","author":[{"given":"Yu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Institute of Big Data Analysis and Applied Mathematics, Hubei University of Education, Wuhan 430205, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiqi","family":"Chen","sequence":"additional","affiliation":[{"name":"Institute of Scientific Research, Nanjing University of Finance & Economics, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1080\/01621459.1986.10478274","article-title":"Nonparametric estimates of the relation between weather and electricity sales","volume":"81","author":"Engle","year":"1986","journal-title":"J. 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