Suppose that there are two populations which are mixed in proportions \(\lambda \) and \((1-\lambda )\), respectively, and an investigator wishes to classify an individual into one of these two populations based on a p-dimensional observation on the individual. This is the basic classification problem with applications in wide variety of fields. In practice, the optimal rule (Bayes rule) is not available and thus need to be estimated when either the densities of the populations or the mixing proportion \(\lambda \) are not completely specified. This paper presents a nonparametric classification procedure based on kernel estimates for the most general case that both the densities and the mixing proportion are unknown. The error rate of the proposed procedure is calculated and compared with that of the optimal rule. Convergence rate of the difference in error rate are also established. A Monte Carlo simulation study and a real data example are given to compare the proposed rule with the optimal rule for a variety of cases.

中文翻译：

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非参数混合模型的经验分类程序

假设有两个群体其在比例混合\（\拉姆达\）和\（（1- \拉姆达）\） ，分别和研究者希望基于一个个体以分类为这两个群体中的一个p -对个体的尺寸观察。这是广泛领域中应用的基本分类问题。在实践中，最佳规则（贝叶斯规则）不可用，因此需要在总体密度或混合比例\（\ lambda \）时进行估算没有完全指定。本文针对密度和混合比例均未知的最一般情况，提出了一种基于核估计的非参数分类程序。计算所提出程序的错误率，并将其与最佳规则的错误率进行比较。还建立了误差率差异的收敛率。给出了蒙特卡洛模拟研究和一个真实的数据示例，以将建议的规则与各种情况下的最佳规则进行比较。