This paper develops a varying-coefficient approach to the estimation and testing of regression quantiles under randomly truncated data. In order to handle the truncated data, the random weights are introduced and the weighted quantile regression (WQR) estimators for nonparametric functions are proposed. To achieve nice efficiency properties, we further develop a weighted composite quantile regression (WCQR) estimation method for nonparametric functions in varying-coefficient models. The asymptotic properties both for the proposed WQR and WCQR estimators are established. In addition, we propose a novel bootstrap-based test procedure to test whether the nonparametric functions in varying-coefficient quantile models can be specified by some function forms. The performance of the proposed estimators and test procedure are investigated through simulation studies and a real data example.

中文翻译：

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具有随机截断数据的变系数模型的加权分位数回归和检验

本文开发了一种变系数方法，用于在随机截断的数据下估计和测试回归分位数。为了处理截断的数据，引入了随机权重，并提出了用于非参数函数的加权分位数回归（WQR）估计器。为了获得良好的效率特性，我们针对变系数模型中的非参数函数进一步开发了加权复合分位数回归（WCQR）估计方法。建立了拟议的WQR和WCQR估计量的渐近性质。此外，我们提出了一种新颖的基于引导程序的测试程序，以测试变系数分位数模型中的非参数函数是否可以由某些函数形式指定。