A note on the multivariate linear model with constraints on the dependent vector

N. I. Fisher*, H. M. Hudson

*Corresponding author for this work

    Research output: Contribution to journalArticle

    Abstract

    It is shown that the least squares estimators of B and Σ in the multivariate linear model {EYi=X1B, D(Yi) =Σ, 1 ≤i≤n, Y1Yn uncorrelated} subject to the constraints YiM=XiN are just the usual least squares estimators B̂= (X'X)‐1X'Y and ΣC = 1/n(Y‐XB̂)(Y‐XB̂) in the unconstrained model where Σ has full rank. Tests of hypotheses concerning B are discussed for situations in which each Yi has a multivariate normal distribution, and examples of the applicability of the model reviewed.

    Original languageEnglish
    Pages (from-to)75-78
    Number of pages4
    JournalAustralian Journal of Statistics
    Volume22
    Issue number1
    DOIs
    Publication statusPublished - 1980

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