有偏估计与LS估计的比较与选择  

Comparison and Selection between Biased Estimator and LS Estimator

作　　者：归庆明[1] 李国重[2] 欧吉坤[1] 

机构地区：[1]中国科学院测量与地球物理研究所,湖北武汉430077 [2]信息工程大学测绘学院,河南郑州450052

出　　处：《测绘学报》2003年第1期26-30,共5页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金资助项目(40074006);国家杰出青年科学基金资助项目(49825107;40125013)

摘　　要：从假设检验的角度研究测量平差Gauss Markov模型中有偏估计与LS估计的选择问题。首先在均方误差准则下对目前应用最广泛的2种有偏估计———岭估计和主成分估计与LS估计进行了比较研究,得到了岭估计、主成分估计优于LS估计的条件;然后运用统计方法对这些条件的成立进行了假设检验;最后通过数值实验说明,在一定显著性水平下当原假设被接受时,说明没有理由不相信采用有偏估计来代替LS估计的合理性,可认为采用有偏估计将对LS估计做出比较有效的改进,当原假设被拒绝时,说明对采用有偏估计的优越性产生了怀疑,此时建议仍采用LS估计。The problem of selection between biased estimator and LS estimator in GaussMarkov model is studied by using the hypothesis testing approach. Firstly, the comparisons between the two most important biased estimators, ordinary ridge estimator and principal components estimator, and LS estimator are conducted by using the criterion of mean squared error; and the conditions to show the superiority of each of these two estimators over the LS estimator have been obtained. Then, the tests have been suggested to verify whether or not these conditions hold in given situations by using the statistical method. Finally, the computational results demonstrate that if the null hypothesis is accepted with a significance level, we have to believe the reasonability of biased estimator instead of LS estimator and we can think if we use the biased estimator it will improve LS estimator more effectively. On the contrary, if the null hypothesis is rejected, we will suspect the biased estimator's superiority. In this case, using the LS estimator is still a good way. 

关 键 词：LS估计 有偏估计 均方误差 假设检验 岭估计 测量平差 主成分估计 

分 类 号：P207[天文地球—测绘科学与技术]