| 线性模型中基于SVD的一个新的有偏估计类 |
| |
| 引用本文： | 归庆明,段清堂,郭建锋,周巧云.线性模型中基于SVD的一个新的有偏估计类[J].数学季刊,2003,18(1). |
| |
| 作者姓名： | 归庆明 段清堂 郭建锋 周巧云 |
| |
| 作者单位： | 1.Institute of Geodesy and Geophysis，Chinese Academy of Sciences，Wuhan 430077，China; 2.Institute of Surveying and Mapping，Information Engineering University，Zhengzhou 450052，China;3.Department of Basic Courses，Zhengzhou College of Light Industry，Zhengzhou 450002，China;4. Department of Basic Courses，Henan Institute of Finance Management，Zhengzhou 450003，China |
| |
| 基金项目： | SupportedbytheNationalScienceFundofChinaforDistingusiheYoungScholarsofChina(4 0 12 50 13,4 9 82 510 7)，SupportedbytheNaturalScienceFoundationofChina(4 0 0 74 0 0 6)，SupportedbytheNaturalScienceFoundationofHenanProvince(0 0 4 0 5130 0 ) |
| |
| 摘 要： | §1 . IntroductionTheproblemofill_conditioninganditsstatisticalconsequencesonalinearregressionmodelarewell_knowninstatistics(Vinod&Ullah 1981;Belsley 1991) .Itis,forinstance ,knownthatoneofthemajorconsequencesofill_conditioningontheleastsquares(LS)regressionesti matoristhattheestimatorproduceslargesamplingvariance,whichinturnmightinappropri atelyleadtoexclusionofotherwisesignificantcoefficientfromthemodel,andthesignsofcoef ficientscanbecontrarytointuitionetc..Tocircumventthisproblem ,manybi…
|
A Class of Biased Estimators Based on SVD in Linear Model |
| |
| GUI Qing-ming,DUAN Qing-tang,GUO Jian-feng,ZHOU Qiao-yun.A Class of Biased Estimators Based on SVD in Linear Model[J].Chinese Quarterly Journal of Mathematics,2003,18(1). |
| |
| Authors: | GUI Qing-ming DUAN Qing-tang GUO Jian-feng ZHOU Qiao-yun |
| |
| Abstract: | In this paper, a class of new biased estimators for linear model is proposed by modifying the singular values of the design matrix so as to directly overcome the difficulties caused by ill_conditioning in the design matrix. Some important properties of these new estimators are obtained. By appropriate choices of the biased parameters, we construct many useful and important estimators. An application of these new estimators in three_dimensional position adjustment by distance in a spatial coordiate surveys is given. The results show that the proposed biased estimators can effectively overcome ill_conditioning and their numerical stabilities are preferable to ordinary least square estimation. |
| |
| Keywords: | ill_conditioning singular value decomposition biased estimation |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
