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The Structure of a Linear Model: Sufficiency, Ancillarity, Invariance, Equivariance, and the Normal Distribution

✍ Scribed by Wolfgang Bischoff

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
176 KB
Volume
73
Category
Article
ISSN
0047-259X

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✦ Synopsis

Consider a general linear model Y=X;+Z where Cov Z may be known only partially. We investigate carefully the notions of sufficiency, ancillarity, invariance, and equivariance and related notions for projectors in a general linear model. In this way we can prove a Basu type theorem. This result can be used to give the relation between the sufficiency of the generalized least-squares estimator and the assumption that Z is normally distributed. So we can generalize the well-known result that the generalized least-squares estimator is sufficient for ; if Z is normally distributed. Further we can solve the converse problem as well.

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