@article{hu_yao_wu_2017, title={The robust EM-type algorithms for log-concave mixtures of regression models}, volume={111}, ISSN={["1872-7352"]}, DOI={10.1016/j.csda.2017.01.004}, abstractNote={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.}, journal={COMPUTATIONAL STATISTICS & DATA ANALYSIS}, author={Hu, Hao and Yao, Weixin and Wu, Yichao}, year={2017}, month={Jul}, pages={14–26} }
 @article{hu_wu_yao_2016, title={Maximum likelihood estimation of the mixture of log-concave densities}, volume={101}, ISSN={["1872-7352"]}, DOI={10.1016/j.csda.2016.03.002}, abstractNote={Finite mixture models are useful tools and can be estimated via the EM algorithm. A main drawback is the strong parametric assumption about the component densities. In this paper, a much more flexible mixture model is considered, which assumes each component density to be log-concave. Under fairly general conditions, the log-concave maximum likelihood estimator (LCMLE) exists and is consistent. Numeric examples are also made to demonstrate that the LCMLE improves the clustering results while comparing with the traditional MLE for parametric mixture models.}, journal={COMPUTATIONAL STATISTICS & DATA ANALYSIS}, author={Hu, Hao and Wu, Yichao and Yao, Weixin}, year={2016}, month={Sep}, pages={137–147} }