L曲线法在等价权抗差岭估计模型中的应用

摘要

An equivalent weight robust ridge estimation model is derived according to the idea of robust estimation for correlated observations, and then the L-curve method is introduced to this model for the solution of ridge parameters. In the iterative process, equivalent weight matrix may be non positive definite so it can not be unitized through classical Cholesky decomposition. According to the characteristic of bifactor model, an algorithm of equivalent weight matrix decomposition is proposed to solve this problem, then the L-curve method can be successfully used in this process. The calculated example manifests that this model can effectively eliminate the influence of coefficient matrix' s morbidity and gross errors.%借鉴相关抗差估计的思想,导出一种基于相关观测的等价权抗差岭估计模型,将L曲线法引入该模型中用于岭参数的求解.针对抗差迭代过程中等价权阵可能不正定而无法使用经典Cholesky分解进行单位化的问题,根据双因子模型的特点,提出一种等价权阵的分解算法对等价权阵进行单位化,使得L曲线法在迭代过程中得以成功运用.算例结果表明:该模型能够有效克服系数阵病态和粗差的影响.