K.U.Leuven, Faculty of Economics and Applied Economics : Department of Economics
CES - Discussion paper series (DPS) 03.16 pages:1-20
A regression estimator is said to be robust if it is still reliable in the presence of outliers. On the other hand, its standard error is said to be robust if it is still reliable when the regression errors are autocorrelated and/or heteroskedastic. This paper shows how robust
standard errors can be computed for several robust estimators of regression, including MMestimators.
The improvement relative to non-robust standard errors is illustrated by means of large-sample bias calculations, simulations, and a real data example. It turns out that
non-robust standard errors of robust estimators may be severely biased. However, if autocorrelation
and heteroscedasticity are absent, non-robust standard errors are more e.cient than the robust standard errors that we propose. We therefore also present a test of the
hypothesis that the robust and non-robust standard errors have the same probability limit.