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Mixtures of multivariate contaminated normal regression models
Statistical Papers ( IF 1.3 ) Pub Date : 2017-11-13 , DOI: 10.1007/s00362-017-0964-y
Angelo Mazza , Antonio Punzo

Mixtures of regression models (MRMs) are widely used to investigate the relationship between variables coming from several unknown latent homogeneous groups. Usually, the conditional distribution of the response in each mixture component is assumed to be (multivariate) normal (MN-MRM). To robustify the approach with respect to possible elliptical heavy-tailed departures from normality, due to the presence of mild outliers, the multivariate contaminated normal MRM is here introduced. In addition to the parameters of the MN-MRM, each mixture component has a parameter controlling the proportion of outliers and one specifying the degree of contamination with respect to the response variable(s). Crucially, these parameters do not have to be specified a priori, adding flexibility to our approach. Furthermore, once the model is estimated and the observations are assigned to the groups, a finer intra-group classification in typical points and (mild) outliers, can be directly obtained. Identifiability conditions are provided, an expectation-conditional maximization algorithm is outlined for parameter estimation, and various implementation and operational issues are discussed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments and compared with other procedures. The performance of this novel family of models is also illustrated on artificial and real data, with particular emphasis to the application in allometric studies.

中文翻译:

多元污染正态回归模型的混合

回归模型的混合 (MRM) 被广泛用于研究来自几个未知潜在同质组的变量之间的关系。通常,假设每个混合分量中响应的条件分布为(多元)正态 (MN-MRM)。为了在可能的椭圆重尾偏离正态时加强该方法,由于存在轻度异常值,这里引入了多变量污染正态 MRM。除了 MN-MRM 的参数之外,每个混合成分都有一个参数控制异常值的比例,一个参数指定响应变量的污染程度。至关重要的是,这些参数不必事先指定,从而为我们的方法增加了灵活性。此外,一旦估计模型并将观察值分配给组,就可以直接获得典型点和(轻度)异常值的更精细的组内分类。提供了可识别性条件,概述了用于参数估计的期望条件最大化算法,并讨论了各种实现和操作问题。回归系数估计量的性质通过蒙特卡罗实验进行评估,并与其他程序进行比较。这个新型模型系列的性能也在人工和真实数据上得到说明,特别强调在异速生长研究中的应用。概述了用于参数估计的期望条件最大化算法,并讨论了各种实现和操作问题。回归系数估计量的性质通过蒙特卡罗实验进行评估,并与其他程序进行比较。这个新型模型系列的性能也在人工和真实数据上得到说明,特别强调在异速生长研究中的应用。概述了用于参数估计的期望条件最大化算法,并讨论了各种实现和操作问题。回归系数估计量的性质通过蒙特卡罗实验进行评估,并与其他程序进行比较。这个新型模型系列的性能也在人工和真实数据上得到说明,特别强调在异速生长研究中的应用。
更新日期:2017-11-13
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