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Biometrika 1982 69(3):679-680; doi:10.1093/biomet/69.3.679
© 1982 by Biometrika Trust
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MISCELLANEA

A sufficient condition on the covariance matrix for F tests in linear models to be valid

S. JEYARATNAM

Department of Mathematics, Southern Illinois University Carbondale, Illinois, U.S.A

Consider the linear model for the random vector Y distributed in N(Xß, C); X is not necessarily of full rank and C is a nonnegative-definite matrix. This note gives a sufficient condition on C for the usual F test of a null hypothesis Hß = 0 to be valid. A discussion of necessity of the condition is included.

Key Words: Estimable function • g-inverse


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