Clustering of subsample means based on pairwise L1 regularized empirical likelihood

Abstract

To classify a vast amount of strata or subsamples with unknown families of distributions according to their strata-means, a clustering approach is developed based on pairwise $$L_1$$ regularized empirical likelihood. Under such a clustering approach, all possible contradictory conclusions are ruled out automatically. On the contrary, the decision rules based on many existing pairwise comparison procedures can generate contradictory results. Moreover, under certain mild conditions, the proposed clustering method enjoys the consistency property that with probability going to one, all strata are classified correctly. An exterior point algorithm is presented for the clustering. The applications of the proposed methods are demonstrated using stock market data and microarray data of breast cancer patients.