  We study the estimation of the linear discriminant with projection pursuit, a
method that is blind in the sense that it does not use the class labels in the
estimation. Our viewpoint is asymptotic and, as our main contribution, we
derive central limit theorems for estimators based on three different
projection indices, skewness, kurtosis and their convex combination. The
results show that in each case the limiting covariance matrix is proportional
to that of linear discriminant analysis (LDA), an unblind estimator of the
discriminant. An extensive comparative study between the asymptotic variances
reveals that projection pursuit is able to achieve efficiency equal to LDA when
the groups are arbitrarily well-separated and their sizes are reasonably
balanced. We conclude with a real data example and a simulation study
investigating the validity of the obtained asymptotic formulas for finite
samples.
