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THE MINIMUM DISTANCE CONSISTENT 2 SLS ESTIMATOR OF THE STRUCTURAL DISTURBANCE VARIANCE
Author(s) -
Kymn Kern O.
Publication year - 1976
Publication title -
metroeconomica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.256
H-Index - 29
eISSN - 1467-999X
pISSN - 0026-1386
DOI - 10.1111/j.1467-999x.1976.tb00554.x
Subject(s) - minimum variance unbiased estimator , estimator , bias of an estimator , mathematics , consistency (knowledge bases) , invariant estimator , stein's unbiased risk estimate , efficient estimator , consistent estimator , residual , statistics , variance (accounting) , minimum mean square error , mean squared error , covariance , minimum distance , economics , algorithm , geometry , accounting
A bstract Let Σ represent the covariance matrix of the structural disturbances. Following Theil the standard consistent estimator of the elements of Σ is given as the mean 2 SLS residual sum of squares. This paper shows the fact that there is a class of consistent estimators of Σ and that the standard estimator is not a minimum distance estimator. It derives the minimum distance consistent 2 SLS estimator of Σ. Then the paper suggests that the derived estimator be applied in the second stage as well as in the third stage of 3 SLS estimation. Other possible applications are indicated. This paper contains an improvement and reformulation of the results previously derived by the author on a related subject that appeared in Metroeconomica [9]. This paper contains an improvement over the previous result in that the derived estimator in this paper possesses not only consistency but also the minimum distance property.