岭-主成分组合估计及其在测量平差中的应用

Combining Ridge and Principal Component Estimation and Its Applications in Survey Adjustment

在分析岭估计缺陷的基础上,运用主成分估计方法,提出了测量平差Gauss-Markov模型参数的一个新的有偏估计,称为岭-主成分组合估计,在均方误差意义下讨论了岭-主成分组合估计的优良性质及其岭-主成分组合估计与岭估计、主成分估计的比较问题,讨论了岭-主成分组合估计中偏参数的选取问题,得到了许多重要结论。理论分析和计算结果都表明,岭-主成分组合估计是一类很有潜力的有偏估计。

In this paper,based on analyzing ordinary ridge estimation properties,a new biased estimation of unknown parameters called combining ridge and principal component(CRPC)estimation is generat-ed for Gauss-Markov model by using the principal component estimation method.The CRPC estima-tion can overcome the defect of the ordinary ridge estimation and the principal component estimation.Its good properties in the mean squared error and under the Pitman's measure of closeness are discussed.Comparative results of mean squared error of these biased estimations are given.The determination of biased parameter in the CRPC estimation is discussed,and some important conclusions are obtained.Theoretic and computational results demonstrate that the CRPC estimation is a potential biased estima-tion.