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The Instrumental Weighted Variables. Part I. Consistency
January 18, 2008 17:22

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 V??ek (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.

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Tags: instrumental, variables, implicit, weighting
The Instrumental Weighted Variables. Part II. Square root of n-consistency
January 18, 2008 17:22

The definition of Instrumental Weighted Variables (IWV) (which is a robust version of the classical Instrumental Variables) and conditions for the weak consistency as given in the Part I of this paper are recalled. The reasons why the classical Instrumental Variables were introduced as well as the idea of implicit weighting the residuals (firstly employed by the Least Weighted Squares, see V??ek (2000)) are also recalled. Then square root of n-consistency of all solutions of the corresponding normal equations is proved.

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Tags: instrumental, variables, implicit, weighting
The Instrumental Weighted Variables. Part III. Asymptotic Representation.
January 18, 2008 17:23

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.

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Tags: instrumental, variables, implicit, weighting