Additive models for extremal quantile regression with Pareto-type distributions
Additive models for extremal quantile regression with Pareto-type distributions
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DOI：
10.1007/s10182-020-00386-1
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
Takuma Yoshida
中科院分区：
文献类型：
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作者：
Takuma Yoshida
估计分布尾部的条件分位数是一个重要的应用问题。然而，数据稀疏性表明，尾部行为的预测比平均值或中心分位数更困难，特别是当使用多变量协变量时。由于可加性模型是多元回归的有效方法，本研究考虑了极值分位数回归的可加性模型。条件分位数函数首先使用中间阶（不太极端）分位数的两阶段估计方法进行估计。随后，通过从中间阶分位数估计外推来构造极阶分位数估计。结合渐近和极值理论，讨论了中阶和极值阶分位数估计的理论性质。进行了模拟研究，以确认性能的估计，并使用真实的数据的应用程序提供。
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.