Robust linear regression using smooth adaptive estimators
Titel:
Robust linear regression using smooth adaptive estimators
Auteur:
Lo, Shu-chuan Han, Chien-Pai
Verschenen in:
Communications in statistics
Paginering:
Jaargang 26 (1997) nr. 1 pagina's 1-19
Jaar:
1997
Inhoud:
In this paper we propose a robust simple linear regression method, namely the smooth adaptwe line (SAL), which divides the data set into three equal groups on the basis of the ordered values of the explanatory variable. The estimators of the slope and intercept are obtained by using the smooth adaptive estimators (SA) (Han and Hawkins 1994) of thc threc groups. The estimators are compared with the least squares (LS) estimators and two other three-group estimators, the resistant line (RL) method (Tukey 1970) and the Bartlett's line (BL) method (Bartlett 1949). A Monte Carlo study is used to study their biases and relative efficiencies for the cases with and without outliers under either normality or non-normality assumption. When there is no outlier or one outlier or small outliers, SAL dominates RL for distributions with tails lighter than t3. Also, SAL dominates BL except for small sample size, say n = 10. To compare SAL with LS, it is known that under normality assumption and no outlier, LS is the best. However, when there are outliers, SAL dominates LS when the outliers are in the x-direction or there are large outliers in the y-direction.
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