Large-sample properties of unsupervised estimation of the linear discriminant using projection pursuit

We study the estimation of linear discriminant with projection pursuit, a method that is unsupervised in sense it does not use class labels estimation. Our viewpoint asymptotic and, as our main contribution, we derive central limit theorems for estimators based on three different indices, skewness, kurtosis, and their convex combination. The results show each case limiting covariance matrix proportional to analysis (LDA), supervised estimator discriminant. An extensive comparative between variances reveals pursuit gets arbitrarily close efficiency LDA when distance groups large enough proportions are reasonably balanced. Additionally, consistent can be achieved also high-dimensional regimes where dimension grows at suitable rate sample size, example, pn=o(n1∕3) sufficient under skewness-based pursuit. conclude real data example simulation investigating validity obtained formulas finite samples.