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A class of finite mixture of quantile regressions with its applications

机译：一类分位数回归的有限混合及其应用

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摘要

Mixture of linear regression models provide a popular treatment for modeling nonlinear regression relationship. The traditional estimation of mixture of regression models is based on Gaussian error assumption. It is well known that such assumption is sensitive to outliers and extreme values. To overcome this issue, a new class of finite mixture of quantile regressions (FMQR) is proposed in this article. Compared with the existing Gaussian mixture regression models, the proposed FMQR model can provide a complete specification on the conditional distribution of response variable for each component. From the likelihood point of view, the FMQR model is equivalent to the finite mixture of regression models based on errors following asymmetric Laplace distribution (ALD), which can be regarded as an extension to the traditional mixture of regression models with normal error terms. An EM algorithm is proposed to obtain the parameter estimates of the FMQR model by combining a hierarchical representation of the ALD. Finally, the iterated weighted least square estimation for each mixture component of the FMQR model is derived. Simulation studies are conducted to illustrate the finite sample performance of the estimation procedure. Analysis of an aphid data set is used to illustrate our methodologies.
机译：线性回归模型的混合为建模非线性回归关系提供了一种流行的方法。回归模型混合的传统估计基于高斯误差假设。众所周知，这种假设对异常值和极值敏感。为了克服这个问题，本文提出了一类新的分位数回归有限混合（FMQR）。与现有的高斯混合回归模型相比，建议的FMQR模型可以为每个组件的响应变量的条件分布提供完整的规范。从可能性的观点来看，FMQR模型等效于基于遵循非对称拉普拉斯分布（ALD）的误差的回归模型的有限混合，这可以看作是对传统的具有正态误差项的回归模型的扩展。提出了一种EM算法，通过结合ALD的层次表示来获得FMQR模型的参数估计。最后，得出FMQR模型的每个混合分量的迭代加权最小二乘估计。进行仿真研究以说明估计程序的有限样本性能。蚜虫数据集的分析用于说明我们的方法。

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