一种线性模型中的稳健估计方法

A ROBUST ESTIMATION METHOD IN LINEAR MODEL

本文讨论了线性模型Y=AX+V中的稳健参数估计，假定观测误差V=（v_1，v_2，…，v_n）~T中有m个（m＜＜n）为粗差（位置未知），服从分布N（0，λσ~2）（λ充分大），其余n-m个服从分布N（0，σ~2）（σ~2已知），在该统计模型的基础上，导出本文的稳健估计方法，为消除对杠杆点处异常值的伪装，文中提出了再次迭代算法。经模拟计算表明，该稳健估计方法与Huber方法、Hampel方法等相比较，有较快的收敛速度和较强的辨识小粗差的能力，再次迭代算法对辨识杠杆点处的异常值是有效的。

This paper deals with the estimation of robust parameters in linear model Y=AX +V. Supposing among observational errors V=(v1, v2,..., vn). there exist m gross er- rors (m<<n) which are subject to distribution N(0, λσ2) (λ being sufficiently large). the remainding n-m errors are subject to distribution N(0,σ2) (σ2 being known). Based on this statistical modle. a robust estimation method is presented. Also suggested is a re-iter- ation algorithm to remove the mask of the outliers at leverage points. Simulation com- putations indicated that this robust estimation method has faster convergence rate and stronger ability of identifying smaller gross errors oyer Huber' and Hample' methods, andthe re-iteration algorithm is certainly very effective for identifying outliers at leverage points.