{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T14:47:17Z","timestamp":1775227637579,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T00:00:00Z","timestamp":1698192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSF of Anhui Province","award":["2008085MA14"],"award-info":[{"award-number":["2008085MA14"]}]},{"name":"NSF of Anhui Province","award":["2108085MA06"],"award-info":[{"award-number":["2108085MA06"]}]},{"name":"NSF of Anhui Province","award":["2023xjzlgc232"],"award-info":[{"award-number":["2023xjzlgc232"]}]},{"name":"NSF of Anhui Province","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"Quality Engineering Project of Anhui University","award":["2008085MA14"],"award-info":[{"award-number":["2008085MA14"]}]},{"name":"Quality Engineering Project of Anhui University","award":["2108085MA06"],"award-info":[{"award-number":["2108085MA06"]}]},{"name":"Quality Engineering Project of Anhui University","award":["2023xjzlgc232"],"award-info":[{"award-number":["2023xjzlgc232"]}]},{"name":"Quality Engineering Project of Anhui University","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"NSERC Discovery","award":["2008085MA14"],"award-info":[{"award-number":["2008085MA14"]}]},{"name":"NSERC Discovery","award":["2108085MA06"],"award-info":[{"award-number":["2108085MA06"]}]},{"name":"NSERC Discovery","award":["2023xjzlgc232"],"award-info":[{"award-number":["2023xjzlgc232"]}]},{"name":"NSERC Discovery","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"the Interior Universities Research Coalition","award":["2008085MA14"],"award-info":[{"award-number":["2008085MA14"]}]},{"name":"the Interior Universities Research Coalition","award":["2108085MA06"],"award-info":[{"award-number":["2108085MA06"]}]},{"name":"the Interior Universities Research Coalition","award":["2023xjzlgc232"],"award-info":[{"award-number":["2023xjzlgc232"]}]},{"name":"the Interior Universities Research Coalition","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"the BC Ministry of Health","award":["2008085MA14"],"award-info":[{"award-number":["2008085MA14"]}]},{"name":"the BC Ministry of Health","award":["2108085MA06"],"award-info":[{"award-number":["2108085MA06"]}]},{"name":"the BC Ministry of Health","award":["2023xjzlgc232"],"award-info":[{"award-number":["2023xjzlgc232"]}]},{"name":"the BC Ministry of Health","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]},{"name":"the University of British Columbia Okanagan (UBC-O) Vice Principal Research in collaboration with the UBC-O Irving K. Barber Faculty of Science","award":["2008085MA14"],"award-info":[{"award-number":["2008085MA14"]}]},{"name":"the University of British Columbia Okanagan (UBC-O) Vice Principal Research in collaboration with the UBC-O Irving K. Barber Faculty of Science","award":["2108085MA06"],"award-info":[{"award-number":["2108085MA06"]}]},{"name":"the University of British Columbia Okanagan (UBC-O) Vice Principal Research in collaboration with the UBC-O Irving K. Barber Faculty of Science","award":["2023xjzlgc232"],"award-info":[{"award-number":["2023xjzlgc232"]}]},{"name":"the University of British Columbia Okanagan (UBC-O) Vice Principal Research in collaboration with the UBC-O Irving K. Barber Faculty of Science","award":["RGPIN 2022-03264"],"award-info":[{"award-number":["RGPIN 2022-03264"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper considers a new mean-variance model with strong mixing errors and describes a combination test for the mean shift and variance change. Under some stationarity and symmetry conditions, the important limiting distribution for a combination test is obtained, which can derive the limiting distributions for the mean change test and variance change test. As an application, an algorithm for a three-step method to detect the change-points is given. For example, the first step is to test whether there is at least a change-point. The second and third steps are to detect the mean change-point and the variance change-point, respectively. To illustrate our results, some simulations and real-world data analysis are discussed. The analysis shows that our tests not only have high powers, but can also determine the mean change-point or variance change-point. Compared to the existing methods of cpt.meanvar and mosum from the R package, the new method has the advantages of recognition capability and accuracy.<\/jats:p>","DOI":"10.3390\/sym15111975","type":"journal-article","created":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T02:40:07Z","timestamp":1698288007000},"page":"1975","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Combination Test for Mean Shift and Variance Change"],"prefix":"10.3390","volume":"15","author":[{"given":"Min","family":"Gao","sequence":"first","affiliation":[{"name":"School of Big Data and Statistics, Anhui University, Hefei 230601, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7981-0708","authenticated-orcid":false,"given":"Xiaoping","family":"Shi","sequence":"additional","affiliation":[{"name":"Irving K. Barber Faculty of Science, University of British Columbia, Kelowna, BC V1V 1V7, Canada"}]},{"given":"Xuejun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Big Data and Statistics, Anhui University, Hefei 230601, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0487-5974","authenticated-orcid":false,"given":"Wenzhi","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Big Data and Statistics, Anhui University, Hefei 230601, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1080\/01621459.1925.10502930","article-title":"The application of statistics as an aid in maintaining quality of a manufactured product","volume":"20","author":"Shewhart","year":"1925","journal-title":"J. Amer. Statist. 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