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We study the estimation of the linear discriminant with projection pursuit, amethod that is blind in the sense that it does not use the class labels in theestimation. Our viewpoint is asymptotic and, as our main contribution, wederive central limit theorems for estimators based on three differentprojection indices, skewness, kurtosis and their convex combination. Theresults show that in each case the limiting covariance matrix is proportionalto that of linear discriminant analysis (LDA), an unblind estimator of thediscriminant. An extensive comparative study between the asymptotic variancesreveals that projection pursuit is able to achieve efficiency equal to LDA whenthe groups are arbitrarily well-separated and their sizes are reasonablybalanced. We conclude with a real data example and a simulation studyinvestigating the validity of the obtained asymptotic formulas for finitesamples.

Large-Sample Properties of Blind Estimation of the Linear Discriminant Using Projection Pursuit