Abstract
Suppose that Y 0, …, Yq are q + 1 criterion variates and that X is a p-dimensional column vector of predictor variates. A principal result of this article is the analytical solution of the problem of determining a p × 1 vector b to maximize the correlation ρ(Y 0, b'X) subject to the constraints ρ(Y i, b'X) = Wi, i = 1, …, q, where W 1, … Wq are specified constants. Some frequently encountered selection problems can be solved by applying this result.

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