Hu Hao, Yao Weixin, Wu Yichao
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.
Department of Statistics, University of California, Riverside, California 92521, U.S.A.
Comput Stat Data Anal. 2017 Jul;111:14-26. doi: 10.1016/j.csda.2017.01.004. Epub 2017 Feb 3.
Finite mixture of regression (FMR) models can be reformulated as incomplete data problems and they can be estimated via the expectation-maximization (EM) algorithm. The main drawback is the strong parametric assumption such as FMR models with normal distributed residuals. The estimation might be biased if the model is misspecified. To relax the parametric assumption about the component error densities, a new method is proposed to estimate the mixture regression parameters by only assuming that the components have log-concave error densities but the specific parametric family is unknown. Two EM-type algorithms for the mixtures of regression models with log-concave error densities are proposed. Numerical studies are made to compare the performance of our algorithms with the normal mixture EM algorithms. When the component error densities are not normal, the new methods have much smaller MSEs when compared with the standard normal mixture EM algorithms. When the underlying component error densities are normal, the new methods have comparable performance to the normal EM algorithm.
有限混合回归（FMR）模型可以重新表述为不完全数据问题，并且可以通过期望最大化（EM）算法进行估计。主要缺点是存在较强的参数假设，例如具有正态分布残差的FMR模型。如果模型设定错误，估计可能会有偏差。为了放宽关于分量误差密度的参数假设，提出了一种新方法，该方法仅通过假设分量具有对数凹误差密度来估计混合回归参数，但具体的参数族是未知的。提出了两种用于具有对数凹误差密度的回归模型混合的EM型算法。进行了数值研究，以比较我们的算法与正态混合EM算法的性能。当分量误差密度不是正态时，与标准正态混合EM算法相比，新方法具有小得多的均方误差。当潜在的分量误差密度是正态时，新方法与正态EM算法具有相当的性能。
