一定分布模式下的最优Lp估计

观测数据在一定的分布模式下，需从理论上解决究竟用多大的ｐ值进行Ｌｐ估计（最优ｐ值的确定），本文基于渐近方差整体最小的原则，给出了最优Ｌｐ估计的定义。观测数据中含有粗差（异常值）的扰动，其误差分布可视为污染分布，作者分析了最优ｐ值的大小，结果表明，若观测数据中含有不同大小、数量的粗差，为使Ｌｐ估计差最小，则ｐ将取［１．２，１．５］中的某一定值，Ｌｐ估计结果最优，此结论对测量数据处理具有一定的参考价值

The optimal Lp estimation under prescribed distribution

The main problem for L p estimation is how to determine the optimal value of parameter p in theory under the prescribed distribution of the observational data. The optimal L P estimation has been defined basing on the global minimum of the asymptotic variance, and the optimal value of parameter p has been determined under the contaminated distribution which denotes the observations with outliers disturbed, the results show that the L p estimation with the value of parameter p between 1.2 and 1.5 is the optimal estimation if the data contain different outliers, so the conclusions can be applied in the surveying data processing. The relationship between L p estimation and the universal distribution has been discussed, and the optimal estimation has been derived also; it demonstrates that the results are coincide with those of the maximum likelihood estimation.