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Pre-test estimation in the linear regression model with competing restrictions

Linear Algebra and its Applications
Publication Date
DOI: 10.1016/0024-3795(94)90468-5


Abstract Consider the linear regression model M={ y, Xβ, σ 2 I n } and two sets of competing, not necessarily exact linear restrictions R j> β= r j , j=1, 2. Assume that the linear restrictions are nested, that is, R 1= T R 2 and r 1= Tr 2 for some matrix T. To estimate the vector β, we derive the pre-test estimator b̄, a two stage procedure based on testing the dominance condition which follows the mean squared error matrix comparison of b 1 and b 2, the restricted least squares estimators of β in the model M j ={ y, Xβ| R j = r j , σ 2 I n }, j=1, 2. We investigate statistical properties of the pre-test estimator b̄ and, comparing b̄ with b 1, characterize its optimality under the mean squared error matrix criterion.

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