Gauss-Markov模型参数的岭型广义逆估计及其优良性

Ridge Type-generalized Inverse Estimator of Parameters in Gauss-Markov Model and Its Optimality

本文继续文献 [10 ]的工作 ,进一步讨论了测量平差 Gauss- Markov模型参数岭型广义逆估计的若干性质 ,如允许性、优效性、相对效率、抗干扰性等等 ,得到了许多重要结论。计算结果表明 ,在设计阵呈病态时 ,岭型广义逆估计确能明显改善 L

In paper, starting from the LS estimation, a new biased estimator of unknown parameters in Gauss Markov model, called ridge type generalized inverse estimator (RGIE), is generated by combining the singular value decomposition expression of the design matrix and the ordinary ridge estimation method. Some optimality, such as admissibility, superiority over the LS estimator, relative efficiency, numerical stability, is discussed and some important conclusions are obtained. The computational results demonstrate that the RGI estimator can improve the LS estimator when the design matrix is ill conditioned.