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 $$L_1$$ 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.

中文翻译：

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基于成对 L1 正则化经验似然的子样本均值聚类

为了根据层均值对具有未知分布族的大量层或子样本进行分类，开发了一种基于成对 $$L_1$$L 1 正则化经验似然的聚类方法。在这种聚类方法下，所有可能的矛盾结论都会被自动排除。相反，基于许多现有成对比较程序的决策规则可能会产生相互矛盾的结果。此外，在某些温和条件下，所提出的聚类方法具有一致性属性，即随着概率趋于 1，所有层都被正确分类。提出了一种用于聚类的外点算法。使用股票市场数据和乳腺癌患者的微阵列数据证明了所提出方法的应用。