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On the invariance of certain estimators
Published online by Cambridge University Press: 17 April 2009
Abstract
In this note, Lp estimators for the parameters in the linear model y = Xβ are considered. In particular, it is shown that these estimators are invariant under scale transformations on the dependent variable; that is, if is an Lp estimator for β, then
for any nonzero scalar a. It is shown that this result does not extend to more general transformations on y, and the invariance property does not hold for general nonlinear models.
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- Research Article
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- Copyright © Australian Mathematical Society 1976