摘要
本文给出一种线性模型中参数与方差联合稳健估计的方法,其中参数估计采用具有有限舍弃点的M-估计;关于方差估计,文中提出采用"格拉布斯统计量"与"峰度检验统计量"对残差序列{ri}进行判别,取剔除异常值后的残差样本方差为我们的方差估计,该方差估计方法比已有的取1.483med|ri|为标准差估计的方法,具有计算方便、估计精度高的优点。对异常值的辨识方法,在已有的"格拉布斯统计量"的基础上增加"峰度检验统计量"的判别,使辨识方法的崩溃点由原来不到10%提高到20%以上。
A method of joint estimation of the parameters and the variance σ~2 in the lin- ear model is presented in the paper. The M-estimators with finite rejection points are adopted for estimating the parameters. In order to estimate the variance σ~2, the Grubbs statistics and the Kurtosis test statistics are adopted to test the residual sequence {ri}, and the sample variance of {ri} after discarding the outliers in {ri} is taken as the estimation of σ~2. The above method of estimating σ~2 is less compu- tational demanding and more accurate, compared with the well-known method which takes 1.483med |ri| as the estimation of σ. The breakdown point of the above estimation of σ~2 is more than 20%. However, the breakdown point is less than 10% if only the Grubbs statistic is used.
出处
《天文学报》
CSCD
北大核心
1992年第1期48-55,共8页
Acta Astronomica Sinica
基金
国家自然科学基金
关键词
参数
方差
估计
异常值
Parameters estimate
Variance estimate
Ontlier
