Instrumental weighted variables under heteroscedasticity. Part I – Consistency
The proof of consistency instrumental weighted variables, the robust version of the classical instrumental variables is given. It is proved that all solutions of the corresponding normal equations are contained, with high probability, in a ball, the radius of which can be selected - asymptotically - arbitrarily small. Then also -consistency is proved. An extended numerical study (the Part II of the paper) offers a picture of behavior of the estimator for finite samples under various types and levels...