{"title":"最小二乘估计器的特征:带有因果误差的多变量同调回归模型的错误定义","authors":"Pramita Bagchi, Subhra Dhar","doi":"10.1090/tpms/1210","DOIUrl":null,"url":null,"abstract":"This article investigates some nice properties of the least squares estimator of multivariate isotonic regression function (denoted as LSEMIR), when the model is mis-specified, and the errors are \n\n \n β\n \\beta\n \n\n-mixing stationary random variables. Under mild conditions, it is observed that the least squares estimator converges uniformly to a certain monotone function, which is closest to the original function in an appropriate sense.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characterization of the least squares estimator: Mis-specified multivariate isotonic regression model with dependent errors\",\"authors\":\"Pramita Bagchi, Subhra Dhar\",\"doi\":\"10.1090/tpms/1210\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article investigates some nice properties of the least squares estimator of multivariate isotonic regression function (denoted as LSEMIR), when the model is mis-specified, and the errors are \\n\\n \\n β\\n \\\\beta\\n \\n\\n-mixing stationary random variables. Under mild conditions, it is observed that the least squares estimator converges uniformly to a certain monotone function, which is closest to the original function in an appropriate sense.\",\"PeriodicalId\":42776,\"journal\":{\"name\":\"Theory of Probability and Mathematical Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and Mathematical Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/tpms/1210\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and Mathematical Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/tpms/1210","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Characterization of the least squares estimator: Mis-specified multivariate isotonic regression model with dependent errors
This article investigates some nice properties of the least squares estimator of multivariate isotonic regression function (denoted as LSEMIR), when the model is mis-specified, and the errors are
β
\beta
-mixing stationary random variables. Under mild conditions, it is observed that the least squares estimator converges uniformly to a certain monotone function, which is closest to the original function in an appropriate sense.