新的递推有界GM回归估计算法

A New Recursive Bounded GM Estimator for Regression

提出一种新的递推有界广义极大似然类(GM)回归估计器,新估计器所用的风险函数基于更一般的框架,并采用有界M-估计函数.设计一个新的权函数拒绝或降低异常点对估计结果的影响,并增加一个增广项,提出一种具有较强自适应能力的面向自回归(AR)模型参数估计的算法.仿真结果表明:提出的GM回归估计器及面向AR模型的算法对异常点不利影响(主要来自于回归变量中的加性异常点)的抑制效果均优于其他GM估计器;在参数不做任何调整的情况下,面向AR模型的算法对非平稳环境下的估计具有良好的估计精度和收敛性.

A new recursive bounded GM estimator for regression is proposed. Unlike other GM estimators, the new esti- mator is based on one more general framework and uses a cost function with bounded M-estimate functiorL The new esti- mator, in effect, is a recursive one-step iteration solution of the ＂normal equations＂ corresponding to the cost function. In the new estimator, a weight function is designed to reject or to reduce the influence of the outliers. Furthermore, by in-- troducing an augment variable, the proposed estimator is modified to a very adaptive version for the estimation of autore- gressive parameters. The simulation results show that both the proposed estimator and its modification are more effective than other related estimators in suppressing the adverse influence of outliers; the proposed estimator, with the same set- tings, can keep a high accuracy and stable convergence performance in a variety of non-stationary environments.