A NOTE ON THE MULTIVARIATE LINEAR MODEL WITH CONSTRAINTS ON THE DEPENDENT VECTOR |
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| Authors: | N.I. Fisher H. M. Hudson |
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| Affiliation: | CSIRO Division of Mathematics and Statistics, Lindfield, N.S.W.;School of Economic and Financial Studies, Macquarie University |
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| Abstract: | It is shown that the least squares estimators of B and Σ in the multivariate linear model {E Y i= X 1 B , D ( Y i) =Σ, 1 ≤ i ≤ n , Y 1 Y n uncorrelated} subject to the constraints Y i M = X i N are just the usual least squares estimators = ( X'X )-1 X'Y and ΣC = 1/n( Y-X )( Y-X ) in the unconstrained model where Σ has full rank. Tests of hypotheses concerning B are discussed for situations in which each Y i has a multivariate normal distribution, and examples of the applicability of the model reviewed. |
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