Lp估计的唯一性与无偏性  

THE UNIQUENESS AND UNBIASNESS OF Lp ESTIMATION

作　　者：周世健[1] 臧德彦[1] 张立亭[1] 

机构地区：[1]华东地质学院测量系,江西临川344000

出　　处：《勘察科学技术》2000年第6期50-52,55,共4页Site Investigation Science and Technology

基　　金：国家自然科学基金资助项目! (4 970 10 14)

摘　　要：Lp估计可处理异常值扰动的观测数据 ,但对Lp估计的性质讨论较少 ,该文重点讨论此问题。首先从理论上证明当 1<p <∞和R(A) =t时 ,Lp估计的唯一性 ,如误差分布是对称分布 ,相应的Lp估计为无偏估计 ;若 ρ函数为偶函数和误差分布为对称分布 ,Robust估计用选权迭代进行计算 ,且用反对称估计作为迭代的初始值 ,那么Robust估计也是无偏估计 ;当p =1时 ,作为Robust估计的特例 ,可得相同的结论 。It is well known that the Lp estimation can be used in the processing of the observational data with the outliers distributed, but the statistical properties of the Lp estimation have less discussed. The paper aimed at the problem, the uniqueness of the Lp estimation when 1<p<∞ and R(A)=t has first been theoretically proved in detail, correspondingly, the unbiasness of the Lp estimation being obtained when 1<p<∞ and the error distribution is symmetrical. Based on a symmetrical error distribution and ρ(.) an even function, the robust estimation is unbiased if it is calculated by iterative weighted ieast squares with an antisymmetrical estimation as starting points of iteration. When p=1, the least sum estimation is also unbiased as a special case of the robust estimation.

关 键 词：Lp估计 唯一性 无偏性 Robust估计 反对称估计 观测数据处理 

分 类 号：P207[天文地球—测绘科学与技术]