Franke et al. (1984).
3.3 Multivariate regression
An important application of robust methods in economics concerns the mul-
tivariate regression case. This is relatively straightforward with exogenous
explanatory variables only, see Koenker and Portnoy (1990), Bilodeau and
Duchesne (2000), and Lopuhaa (1992) for the M -, S -, and τ-estimation, re-
spectively. Estimating general simultaneous equations models has to mimick
either three-stage LS or full information MLE (Marrona and Yohai, 1997).
Whereas Koenker and Portnoy (1990) follow with the weighted LAD the first
approach, Krishnakumar and Ronchetti (1997) use M -estimation together
with the second strategy.
3.4 General estimation principles
There are naturally many more model classes, for which one can construct
robust estimation procedures. Since most econometric models can be esti-
mated by means of MLE or GMM, it is however easier to concentrate on
robust counterparts of these two estimation principles. There are other esti-
mation concepts, such as nonparametric smoothing, that can employ robust
estimation (Hardle, 1982), but they go beyong the scope of this chapter.
First, recent contributions to robust MLE can be split to two groups.
One simply defines a weighted maximum likelihood, where weights are com-
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