Robust Econometrics

puted from an initial robust fit (Windham, 1995; Markartou et al., 1997).
Alternatively, some erroneous observations can be excluded completely from
the likelihood function (Clarke, 2000; Marazzi and Yohai, 2004). This ap-
proach requires existence of an initial robust estimate, and thus, it is not
useful for models, for which there are no robust methods available. The
second approach is motivated by the S-estimation, namely LTS, and defines
the maximum trimmed likelihood as an estimator maximizing the product of
the h largest likelihood contribution; that is, those corresponding only to h
most likely observations (Hadi and Luceno, 1997). This estimator was stud-
ied mainly in the context of generalized linear models (Müller and Neykov,
2003), but its consistency is established in a much wider class of models
(Cιzek, 2004).

Second, more widely used GMM also attracted attention from its robust-
ness point of view. A special case, instrumental variable estimation, was stud-
ied, for example, by Wagenvoor and Waldman (2002) and Kim and Muller
(2006). See also Chernozhukov and Hansen (2006) for instrumental variable
quantile regression. More generally, Ronchetti and Trojani (2001) proposed
an M -estimation-based generalization of GMM, studied its robust properties,
and design corresponding tests. This work became a starting point for others,
who extended the methodology of Ronchetti and Trojani (2001) to robustify
simulation-based methods of moments (Genton and Ronchetti, 2003; Ortelli
and Trojani, 2005).

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