尺度参数的Lp估计与精度评定

根据定位参数与尺度参数的联合Ｍ估计，导出了尺度参数的Ｌｐ估计；当ｐ＝２时，与最小二乘估计一致，观测数据服从正态分布时，为最优无偏估计；由于尺度参数Ｌｐ估计的影响函数为无界函数，估计不具抗差性，但把残差Ｗｉｎｓｏｒ化，作者得到了尺度参数的抗差Ｌｐ估计；依据定位参数的协方差阵，可进行Ｌｐ估计的精度评定。这些结果对于Ｌｐ估计的研究和应用具有一定的参考价值。

THE Lp ESTMATION OF THE SCALE PARAMETER AND THE ACCURACY EVALUATION

Based on the theory for joint M estimation of the location parameters and scale parameter, the Lp estimation for the scale parameter has been derived first and the results are the same as the Least Squares estimation which is the best unbiased estimation while p =2; the influence function for Lp estimation of the scale parameter has been obtained, and the estimator has no robustness because the influence function is an unbounded function, the robust Lp estimation of the scale parameter has been proposed using the Winsor's residuals by authors. Finally, the accuracy evaluation of the Lp estimation has been discussed on the light of the Lp estimation of the scale parameter, the results can be applied in the practice; therefore, it is significant to the practice of the surveying data processing.