{"title":"用区间分析计算区间值线性回归模型参数界的最小化方法","authors":"R. Mwangi, H. Imai, Yoshiharu Sato","doi":"10.5183/JJSCS1988.17.21","DOIUrl":null,"url":null,"abstract":"Interval data may appear in perturbed problems or when measured quanties are subject to error. Small errors in data also occur because of roundoff. We have used interval analysis to bound data values and their arithmetic solutions. An algorithm that uses the interval quadratic and Newton methods to enclose minimum values is used in a least-squares objective function. As a result, appropriate bounds for the coefficient of a regression model have been obtained. An example from cardiology in Billard and Diday (2000) is illustrated.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A MINIMIZATION METHOD FOR COMPUTING PARAMETER BOUNDS IN AN INTERVAL VALUED LINEAR REGRESSION MODEL USING INTERVAL ANALYSIS\",\"authors\":\"R. Mwangi, H. Imai, Yoshiharu Sato\",\"doi\":\"10.5183/JJSCS1988.17.21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Interval data may appear in perturbed problems or when measured quanties are subject to error. Small errors in data also occur because of roundoff. We have used interval analysis to bound data values and their arithmetic solutions. An algorithm that uses the interval quadratic and Newton methods to enclose minimum values is used in a least-squares objective function. As a result, appropriate bounds for the coefficient of a regression model have been obtained. An example from cardiology in Billard and Diday (2000) is illustrated.\",\"PeriodicalId\":338719,\"journal\":{\"name\":\"Journal of the Japanese Society of Computational Statistics\",\"volume\":\"15 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Japanese Society of Computational Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5183/JJSCS1988.17.21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Japanese Society of Computational Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5183/JJSCS1988.17.21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A MINIMIZATION METHOD FOR COMPUTING PARAMETER BOUNDS IN AN INTERVAL VALUED LINEAR REGRESSION MODEL USING INTERVAL ANALYSIS
Interval data may appear in perturbed problems or when measured quanties are subject to error. Small errors in data also occur because of roundoff. We have used interval analysis to bound data values and their arithmetic solutions. An algorithm that uses the interval quadratic and Newton methods to enclose minimum values is used in a least-squares objective function. As a result, appropriate bounds for the coefficient of a regression model have been obtained. An example from cardiology in Billard and Diday (2000) is illustrated.
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