成分数据众数回归及其变量选择

Mode Regression of Compositional Data and Its Variable Selection

随着科学技术的发展,高维成分数据广泛出现在医学和经济学等领域且收集越来越方便,惩罚方法是解决高维数据变量选择问题的重要方法。目前关于成分数据变量选择的研究主要基于均值回归,但均值回归不具有稳健性,而众数回归因其对异常值、重尾分布或不对称分布具有稳健性而备受重视。文章研究成分数据众数回归模型的估计与变量选择,提出坐标下降EM算法对目标函数进行求解,在误差服从不同分布下将该方法与已有方法进行比较,并以实例进行了验证。

With the development of science and technology, high-dimensional compositional data are widely used in medical and economic fields and becomes more and more convenient to collect. Penalized techniques are important methods to solve the problem of variable selection in high-dimensional data. Current researches on the variable selection of compositional data are mainly based on mean regression, but mean regression is not robust, while mode regression has attracted much attention because of its robustness to outliers, heavy-tailed distributions or asymmetric distributions. This paper studies the estimation and variable selection of mode regression model of compositional data, proposes the EM algorithm of coordinate descent to solve the objective function, and then compares the proposed method with the existing methods when the errors follow different distributions. Finally,the paper gives an example to make verification.