Recently, Shafaei and Kayid (Statistical Papers, 2017) introduced and studied the bivariate quantile residual life model. It has been shown that two suitable bivariate quantile residual life functions characterize the underlying distribution uniquely. In the current investigation, we first propose a nonparametric estimator of this new model. The estimator is strongly consistent and, on proper normalization, asymptotically follows a bivariate Gaussian process. An extensive simulation study has been conducted to discuss the behavior of the estimator. Finally, to illustrate the applications, a real data set related to a tumor recurrence trial is presented and discussed.

中文翻译：

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应用于肿瘤复发数据集的双变量分位数剩余寿命模型的非参数估计

最近，Shafaei 和 Kayid（Statistical Papers，2017）介绍并研究了双变量分位数剩余寿命模型。已经表明，两个合适的双变量分位数剩余寿命函数独特地表征了潜在的分布。在当前的调查中，我们首先提出了这个新模型的非参数估计量。估计量是高度一致的，并且在适当的归一化时，渐近地遵循二元高斯过程。已经进行了广泛的模拟研究来讨论估计器的行为。最后，为了说明应用，展示并讨论了与肿瘤复发试验相关的真实数据集。