混合回归模型的无监督Liu型收缩估计
Unsupervised Liu-type Shrinkage Estimators for Mixture of Regression Models
摘要：
在许多应用中（例如，医学研究），感兴趣的群体（例如，疾病状态）包括异质亚群。混合概率回归模型是将协变量信息引入总体异质性学习的最常用方法之一。尽管它的灵活性，该模型可能会导致不可靠的估计存在多重共线性问题。在本文中，我们开发了Liu型收缩方法，通过无监督学习方法来估计多重共线性模型的系数。所开发的方法的性能进行评估，通过分类和随机版本的期望最大化算法。数值研究表明，所提出的方法优于他们的岭和极大似然同行。最后，所开发的方法被应用于分析50岁及以上的妇女的骨矿物质数据。
英文摘要：
In many applications (e.g., medical studies), the population of interest (e.g., disease status) comprises heterogeneous subpopulations. The mixture of probabilistic regression models is one of the most common techniques to incorporate the information of covariates into learning of the population heterogeneity. Despite its flexibility, the model may lead to unreliable estimates in the presence of multicollinearity problem. In this paper, we develop Liu-type shrinkage methods through an unsupervised learning approach to estimate the model coefficients in multicollinearity. The performance of the developed methods is evaluated via classification and stochastic versions of EM algorithms. The numerical studies show that the proposed methods outperform their Ridge and maximum likelihood counterparts. Finally, the developed methods are applied to analyze the bone mineral data of women aged 50 and older.
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