In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional predictors, the new semiparametric models can easily incorporate high dimensional predictors into the nonparametric components. The proposed models are very general, and many of the recently proposed semiparametric/nonparametric mixture regression models are indeed special cases of the new models. Backfitting estimates and the corresponding modified EM algorithms are proposed to achieve optimal convergence rates for both parametric and nonparametric parts. We establish the identifiability results of the proposed two models and investigate the asymptotic properties of the proposed estimation procedures. Simulation studies are conducted to demonstrate the finite sample performance of the proposed models. Two real data applications using the new models reveal some interesting findings.

中文翻译：

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基于模型的聚类的单索引回归的半参数混合

在本文中，我们针对基于模型的聚类提出两类具有单索引的半参数混合回归模型。与许多只能用于低维预测变量的半参数/非参数混合回归模型不同，新的半参数模型可以轻松地将高维预测变量合并到非参数组件中。提出的模型非常通用，最近提出的许多半参数/非参数混合回归模型确实是新模型的特殊情况。提出了反向拟合估计和相应的改进EM算法，以实现参数和非参数零件的最优收敛速度。我们建立了所提出的两个模型的可识别性结果，并研究了所提出的估计程序的渐近性质。进行仿真研究以证明所提出模型的有限样本性能。使用新模型的两个实际数据应用揭示了一些有趣的发现。