The Instrumental Weighted Variables. Part III. Asymptotic Representation

The robust version of the classical instrumental variables, called Instrumental Weighted Variables (IWV) and the conditions for its square root of n-consistency as given in the Part I and II of this paper are recalled. Of course, the reasons why the classical instrumental variables as well as IWV were introduced and the idea of implicit weighting the residuals (firstly employed by the Least Weighted Squares, see Víšek (2000)) are also very briefly recalled (details were discussed in Part I of this paper). Then asymptotic representation and normality of all solutions of the corresponding normal equations is proved.