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Identifying interaction effects via additive quantile regression models

机译:通过添加量数回归模型识别交互效应

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摘要

As additive quantile regression (AQR) models possess the properties of robustness and flexibility, they become increasingly popular in many applications. However, such models may fail when predictors reflect interaction effects in the response. In fact, we often encounter such a problem that the main effects are not significant but the pairwise interactions are in regression. The existence of such a situation is neither accidental nor ignorable. Overlooking the interaction effects may render many of the traditional statistical techniques used for studying data relationships invalid. In these situations, it is necessary to consider more reasonable models such as AQR model with pairwise interactions. This paper mainly studies estimation and testing for the AQR model with pairwise interactions. To estimate the unknown functions in the model, local linear fitting and ordinary backfitting methods are applied. The generalized likelihood ratio (GLR) type test statistic is constructed to test the overall significance of pairwise interactions, and bootstrap method is utilized to approximate the asymptotic distribution of the test statistic. Theoretical properties of estimators and GLR type test statistic are derived. Bandwidth selection based on plug-in method for pairwise interactions is discussed as well. Finally, simulation study and a simple empirical analysis are presented to illustrate the performance of the proposed model.
机译:随着添加量分数回归(AQR)模型具有鲁棒性和灵活性的性质,它们在许多应用中越来越受欢迎。然而,当预测器反映响应中的相互作用效应时,这种模型可能会失败。事实上,我们经常遇到这样一个问题,即主要效果不显着,但成对相互作用是回归的。这种情况的存在既不偶然也不是无知的。忽略互动效果可能会呈现用于研究数据关系无效的许多传统统计技术。在这些情况下,有必要考虑更合理的模型,例如具有成对交互的AQR模型。本文主要研究与成对相互作用的AQR模型的估算和测试。为了估计模型中的未知功能,应用了局部线性拟合和普通的应答方法。构建广义似然比(GLR)型测试统计以测试成对相互作用的总体意义,并利用引导方法来近似测试统计的渐近分布。衍生估计和GLR型试验统计的理论特性。还讨论了基于用于成对交互的插件方法的带宽选择。最后,提出了仿真研究和简单的实证分析来说明所提出的模型的性能。

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