Expectile is a generalization of the expected value in probability and statistics. In finance and risk management, the expectile is considered to be an important risk measure due to its connection with gain–loss ratio and its coherent and elicitable properties. Linear multiple expectile regression was proposed in 1987 for estimating the conditional expectiles of a response given a set of covariates. Recently, more flexible nonparametric expectile regression models were proposed based on gradient boosting and kernel learning. In this paper, we propose a new nonparametric expectile regression model by adopting the deep residual network learning framework and name it Expectile NN. Extensive numerical studies on simulated and real datasets demonstrate that Expectile NN has very competitive performance compared with existing methods. We explicitly specify the architecture of Expectile NN so that it is easy to be reproduced and used by others. Expectile NN is the first deep learning model for nonparametric expectile regression.

中文翻译：

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通过深度残差网络进行预期回归

期望是对概率和统计中期望值的概括。在财务和风险管理中，由于期望值与收益率/损失率以及其连贯和可引诱的性质有关，因此期望值被认为是一项重要的风险度量。线性多重期望回归是在1987年提出的，用于在给定一组协变量的情况下估计响应的条件期望。最近，基于梯度提升和核学习提出了更灵活的非参数期望回归模型。在本文中，我们通过采用深度残差网络学习框架，提出了一个新的非参数期望回归模型，并将其命名为Expectile NN。对模拟和真实数据集的大量数值研究表明，Espectile NN与现有方法相比具有非常好的竞争性能。我们明确指定Expectile NN的体系结构，以便易于他人复制和使用。期望神经网络是第一个用于非参数期望回归的深度学习模型。