Abstract
SUMMARY Various extremal results have been proved concerning the efficiency of least squares estimates relative to Gauss-Markov estimates and concerning the canonical correlations between two sets of random variables. In this paper we show how these two types of result are related, and derive a new result from which many previous inequalities can be derived. Some key word8: Canonical correlation; Inefficiency; Least squares. The inequality for the generalized efficiency of least squares estimates relative to best linear unbiased estimates (Bloomfield & Watson, 1975; Knott, 1975) has found applications in other areas. A consequence was used by Venables (1976) in testing for sphericity of a Gaussian distribution, and by Khatri (1978) in proving extremal results for canonical correlations. We shall prove a slightly more general result concerning canonical
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