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Additive models for extremal quantile regression with Pareto-type distributions

机译：具有帕累托式分布的极值分位数回归的附加模型

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摘要

Estimating conditional quantiles in the tail of a distribution is an important problem for several applications. However, data sparsity indicates that the predictions of tail behavior are more difficult compared with those for the mean or center quantiles, in particular, when a multivariate covariate is used. As additive models are known to be an efficient approach for multiple regression, this study considers an additive model for extremal quantile regression. The conditional quantile function is first estimated using a two-stage estimation method for the intermediate-order (not too extreme) quantile. Subsequently, the extreme-order quantile estimator is constructed by extrapolating from the intermediate-order quantile estimator. By combining the asymptotic and extreme value theories, the theoretical properties of the intermediate- and extreme-order quantile estimators are evaluated. A simulation study is conducted to confirm the performance of the estimators, and an application using real data is provided.
机译：在分布尾部估计条件量数是若干应用的重要问题。然而，数据稀疏性表明，与使用多变量协变量的平均值或中心定量相比，尾部行为的预测更困难。由于已知添加剂模型是一种有效的多元回归方法，本研究考虑了极值分位数回归的添加剂模型。首先使用两阶段估计方法来估计条件分位数函数，用于中间阶（不是过度极端）定量。随后，通过从中间阶定量估计器推断来构造极级定量估计器。通过组合渐近和极值理论，评估中间和极衡量级估计器的理论特性。进行了仿真研究以确认估算器的性能，提供使用实际数据的应用程序。

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