抗差主成分估计在单位线推算中的应用

摘要

The Unit Hydrograph is widely used in simulating surface runoff processes.However,the results of least squares estimator are not satisfactory or even unreasonable when the matrix is ill-conditioned or outlier in the observed data.For solving these problems,the Robust Least Squares Estimator and Robust Principal Component Estimate are used and the results are compared with the Least Squares Estimator.The calculation results show that the Robust Principal Component Estimate cannot be able to overcome the ill-conditioned matrix,but can withstand the observations of interference in outliers.%流域汇流单位线的推求常使用最小二乘法,但当法方程系数矩阵病态或是观测值中含有粗差时,用传统的最小二乘法估计的误差会很大.针对这些情况,采用抗差最小二乘法和有偏估计的抗差主成分估计法,与最小二乘估计进行计算比较.计算结果表明,抗差主成分估计不但能够克服法方程系数矩阵病态的影响,而且能够抵御观测值中异常值的干扰,得到光滑合理的单位线.