A Class of Biased Estimators Based on SVD in Linear Model

摘要

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.