**Jan Ámos Víšek**

Charles University in Prague, Faculty of Social Sciences

`visek@mbox.fsv.cvut.cz`

The point estimation was from the very beginning of the statistics
(and econometrics) one of the key topics. In the early days, the
unbiasedness was assumed to play the crucial role but later the *
(weak) consistency* overtook the governance.

The (classical and/or robust) statistics developed a bunch of
``principles'', heuristics of which promised to yield the estimators
being not only consistent but also premiant in a widely considered
competition (achieving e. g. efficiency). Some of them worked, some
not. Typically, the estimator was given as a solution of a (vector)
equation (*normal equations*) - interpretable as -tuple of
orthogonality conditions (of residuals to the columns of design matrix,
e. g.).

The consistency requires orthogonality of residuals to the (estimated)
model and hence the estimators are defined as solution of a -tuple of
orthogonality conditions (). It allows for direct employment of
additional information about the parameter in question. In such a case
we speak about *Generalized Method of Moments estimation*.

Despite the forty years of robust studies, the econometrics haven't taken seriously (possible) fatal consequences of a slight deviation of the assumed model from the underlying one as Fisher did already in 1922 or of a few contaminating observations as considered by Hampel or Huber much later on.

Since the weighting down the order statistics of squared residuals
appeared to be powerful tool for influential-points-recognition, the
present paper offers an idea of the *generalized method of moments
weighted estimators* and shows that *the least weighted squares*
are special case of them.

2005-05-23