{"title":"线性模型","authors":"Cedric E. Ginestet","doi":"10.1201/9781315367002-6","DOIUrl":null,"url":null,"abstract":"1.2 BLUEs Definition 1. Given a random sample, Y1, . . . , Yn ind ∼ f(X,β); an estimator β̂(Y1, . . . , Yn) of the parameter β is said to be unbiased if E[β̂|X] = β, for every β ∈ Rp . Definition 2. An estimator β̂ of a parameter β is said to be Best Linear Unbiased Estimator (BLUE), if it is a linear function of the observed values y, an unbiased estimator of β; and if for any other linear unbiased estimator β̃, we have Var[β̂|X] ≤ Var[β̃|X].","PeriodicalId":286721,"journal":{"name":"Machine Learning Fundamentals","volume":"77 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linear Models\",\"authors\":\"Cedric E. Ginestet\",\"doi\":\"10.1201/9781315367002-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"1.2 BLUEs Definition 1. Given a random sample, Y1, . . . , Yn ind ∼ f(X,β); an estimator β̂(Y1, . . . , Yn) of the parameter β is said to be unbiased if E[β̂|X] = β, for every β ∈ Rp . Definition 2. An estimator β̂ of a parameter β is said to be Best Linear Unbiased Estimator (BLUE), if it is a linear function of the observed values y, an unbiased estimator of β; and if for any other linear unbiased estimator β̃, we have Var[β̂|X] ≤ Var[β̃|X].\",\"PeriodicalId\":286721,\"journal\":{\"name\":\"Machine Learning Fundamentals\",\"volume\":\"77 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Machine Learning Fundamentals\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1201/9781315367002-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Machine Learning Fundamentals","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9781315367002-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
1.2 BLUEs的定义给定一个随机样本Y1，…， Yn ind ~ f(X，β);一个估计量β·(Y1，…，对于每一个β∈Rp，如果E[β∈X] = β，则参数β的Yn)是无偏的。定义2。一个参数β的估计量β·是最佳线性无偏估计量(BLUE)，如果它是观测值y的线性函数，则是β的无偏估计量;对于任何其他的线性无偏估计量，我们有Var[β²|X]≤Var[β²|X]。
1.2 BLUEs Definition 1. Given a random sample, Y1, . . . , Yn ind ∼ f(X,β); an estimator β̂(Y1, . . . , Yn) of the parameter β is said to be unbiased if E[β̂|X] = β, for every β ∈ Rp . Definition 2. An estimator β̂ of a parameter β is said to be Best Linear Unbiased Estimator (BLUE), if it is a linear function of the observed values y, an unbiased estimator of β; and if for any other linear unbiased estimator β̃, we have Var[β̂|X] ≤ Var[β̃|X].
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