Chinese Quarterly Journal of Mathematics ›› 2003, Vol. 18 ›› Issue (1): 82-87.

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A Class of Biased Estimators Based on SVD in Linear Model

  

  1. 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
  • Received:2001-10-09 Online:2003-03-30 Published:2024-04-23
  • About author:GUI Qing-ming(1960-),male,native of Wujiang,Jiangsu,a professor of Information Engineering Univer- sity ,engages in the theory and application of statistics;DUAN Qing-tang(1958-),male,native of Weihui,Henan,an associ- ate professor of Zhengzhou College of Light Industry ,engages in the theory and appliation of statistics;GUO Jian-feng(1972 - ) ,male,native of Changge,Henan,a lecturer of Information Engineering University ,engages in the theory and application of statistics;ZHOU Qiao-yun(1966-),female,native of Wenxian,Henan,a lecturer of Henan Institute of Finance Manage- ment ,engages in the theory and application of mathematics.
  • Supported by:
    Supported by the National Science Fund of China for Distingusihe Young Scholars of China(40125013; 49825107);Supported by the Natural Science Foundation of China(40074006);Supported by the Natural Science Foundation of Henan Province(004051300)

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.

Key words: ill-conditioning, singular value decomposition, biased estimation

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