The Instrumental Weighted Variables. Part I. Consistency

A robust version of the method of Instrumental Variables accommodating the idea of an implicit weighting the residuals is proposed and its properties studied. (The idea of implicit weighting down the “suspicious” residuals was firstly employed by the method of the Least Weighted Squares, see Víšek (2000c).) It means that at first, it is shown that all solutions of the corresponding normal equations are bounded in probability. Finally, the weak consistency of them is proved.