Expectile and quantile regression-David and Goliath?
Expectile and quantile regression-David and Goliath?
复制标题
DOI：
10.1177/1471082x14561155
复制
发表时间：
2015-10-01
影响因子：
1
通讯作者：
Kauermann, Goeran
中科院分区：
文献类型：
--
作者：
Waltrup, Linda Schulze;Sobotka, Fabian;Kauermann, Goeran
最近在现代回归建模的兴趣集中在扩展可用的（平均）回归模型，通过描述更一般的属性的响应分布。另一种方法是分位数回归，其中假设对响应的条件分位数函数的回归效应。分位数回归可以被看作是中位数回归的推广，而期望值回归则是均值回归的推广形式。一般来说，分位数甚至可以提供超过0.5分位数（中位数）的自然解释。一个类似的简单的解释是不可用的预期超过0.5预期，平均值。尽管如此，expectables有一些有趣的特性，其中一些在这篇文章中讨论。我们对比了这两种方法，并展示了如何从一个细网格的预期分位数。我们比较这样的分位数从预期直接分位数估计效率。我们还研究了回归问题，其中分位数和期望曲线都具有相邻曲线可能相互交叉的不良特性。我们提出了一种基于样条的改进方法来估计不相交的期望曲线。在一个应用程序中，我们看看预期的缺口，金融中使用的一种风险度量，它需要估计的期望值和分位数，可以很容易地计算与本文中提出的方法。
Recent interest in modern regression modelling has focused on extending available ( mean) regression models by describing more general properties of the response distribution. An alternative approach is quantile regression where regression effects on the conditional quantile function of the response are assumed. While quantile regression can be seen as a generalization of median regression, expectiles as alternative are a generalized form of mean regression.Generally, quantiles provide a natural interpretation even beyond the 0.5 quantile, the median. A comparable simple interpretation is not available for expectiles beyond the 0.5 expectile, the mean. Nonetheless, expectiles have some interesting properties, some of which are discussed in this article. We contrast the two approaches and show how to get quantiles from a fine grid of expectiles. We compare such quantiles from expectiles with direct quantile estimates regarding efficiency. We also look at regression problems where both quantile and expectile curves have the undesirable property that neighbouring curves may cross each other. We propose a modified method to estimate non-crossing expectile curves based on splines. In an application, we look at the expected shortfall, a risk measure used in finance, which requires both expectiles and quantiles for estimation and which can be calculated easily with the proposed methods in the article.