• 主题
高级搜索  >
历史搜索 清空历史
首页> 美国政府科技报告 >Linear Model Estimation Errors With Estimated Design Parameters
【24h】

Linear Model Estimation Errors With Estimated Design Parameters

机译：具有估计设计参数的线性模型估计误差

获取原文
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The problem of error estimation of parameters b in a linear model,Y = Xb + e, isconsidered when the elements of the design matrix X are functions of an unknown design' parameter vector c. An estimated value e is substituted in X to obtain a derived design matrix X. Even though the usual linear model conditions are not satisfied with k, there are situations in physical applications where the least squares solution to the parameters is used without concern for the magnitude of the resulting error. Such a solution can suffer from serious errors. This paper examines bias and covariance errors of such estimators. Using a first-order Taylor series expansion, we derive approximations to the bias and covariance matrix of the estimated parameters. The bias approximation is a sum of two terms: One is due to the dependence between C and Y; the other is due to the estimation errors of c and is proportional to b, the parameter being estimated. The covariance matrix approximation, on the other hand, is composed of three components: One component is due to the dependence between c and Y; the second is the covariance matrix Sigma b corresponding to the minimum variance unbiased estimator 6, as if the design parameters were known without error; and the third is an additional component due to the errors in the design parameters. It is shown that the third error component is directly proportional to Sigma b'. Thus, estimation of large parameters with wrong design matrix X will have larger errors of estimation. The results are illustrated with a simple linear example.

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号