ELSEVIER Computational Statistics & Data Analysis 23 (1997) 525-540
COMPUTATIONAL
STATISTICS
& DATA ANALYSIS
A comparative study of some robust
methods for coefficient-estimation
in linear regression
S.G. Meintanis, G.S. Donatos*
Departments of Economics, Universityof Athens, Athens, Greece
Received August 1995; revised February 1996
Abstract
Robust regression estimators are known to perform well in the presence of outliers. Although
theoretical properties of these estimators have been derived, there is always a need for empirical
results to assist their implementation in practical situations. A simulation study of four robust
alternatives to the least-squares method is presented within a set of error-distributions which includes
many outlier-generating models. The robustness and efficiency features of the methods are exhibited,
some finite-sample results are discussed in combination with asymptotic properties, and the relative
merits of the estimators are viewed in connection with the tail-length of the underlying error-
distribution.
Keywords: Simulation; Outliers; Heavy-tailed distributions; Least median of Squares; Functional
least squares; Trimmed least squares
1. Introduction
An important issue in linear regression is the performance of coefficient-estima-
tion procedures when the error term is not normally distributed. In such a case, the
least-squares (LS) method has certain disadvantages. A major disadvantage is that
the LS possesses a breakdown point (Donoho and Huber, 1983), which tends to
zero as the sample size increases. Consequently, observations lying far away from
the bulk of the data can cause the LS-estimator to be carried beyond all bounds.
*Corresponding author.
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