L1范估计的巴尔达型检验及其可靠性

根据残差与真误差的Bahadur型关系,L1范估计中, 粗差几乎完全反映到相应的残差上,这就是L1范估计能正确定位粗差的原因.对L2范估计,粗差只是部分地反应到相应残差上,由此会导致粗差误判.根据L1范估计的残差及其方差, 构造了L1范估计的巴尔达检验统计量, 并讨论了L1范估计的可靠性.与L2范估计的可靠性比较,L1范估计的可靠性受多余观测的影响小.

Baarda Test and Its Reliability in L1-Norm Estimation

From the Bahadur-type relation between the true errors and residuals in the L1-norm estimation, it can be seen that the gross errors are almost completely projected onto the corresponding residuals, which is why the gross errors can be correctly located in the L1-norm estimation. But for the L2-norm estimation, the residual only reflects in part the corresponding gross error, which will lead to mistake in locating gross errors. According to the residuals and their variances, the Baarda test statistic based on the L1-norm estimation is constructed, and the reliability is discussed. As compared with the reliability of the L2-norm estimation, that of the L1-norm estimation is a little affected by the variation of the redundancy component.