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Estimated Generalized Least Squares for a Heteroscedastic Regression Model
Author(s) -
Anh V. V.
Publication year - 1982
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1982.tb00831.x
Subject(s) - heteroscedasticity , estimator , mathematics , statistics , generalized least squares , linear regression , consistent estimator , covariance , minimum variance unbiased estimator
Summary This paper considers the general linear regression model yc = X 1 β+u t under the heteroscedastic structure E(u t ) = 0, E(u 2 ) =σ 2 ‐ (X t β) 2 , E(u t u s ) = 0, t æ s, t, s = 1, T. It is shown that any estimated GLS estimator for β is asymptotically equivalent to the GLS estimator under some regularity conditions. A three‐step GLS estimator, which calls upon the assumption E(u t 2 ) =s̀ 2 (X,β) 2 for the estimation of the disturbance covariance matrix, is considered.