Neural Networks for Partially Linear Quantile Regression
Neural Networks for Partially Linear Quantile Regression
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DOI：
10.1080/07350015.2023.2208183
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发表时间：
2021-06
影响因子：
3
通讯作者：
Qixian Zhong;Jane-ling Wang
中科院分区：
文献类型：
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作者：
Qixian Zhong;Jane-ling Wang
深度学习在各种应用中取得了巨大的成功，但它在分位数回归中的应用仍然很少。与非参数平滑方法相比，深度学习方法的一个主要优点是它可以灵活地以更简洁的方式对复杂数据进行建模。然而，尽管深度学习在预测方面取得了突破，但由于其黑箱性质，它并不适合统计推断。在本文中，我们利用深度学习的优势并将其应用于分位数回归，其目标是产生可解释的结果并执行统计推断。我们通过采用基于部分线性分位数回归模型的半参数方法来实现这一点，其中统计推断主要感兴趣的协变量是线性建模的，所有其他协变量都是通过深度神经网络非参数建模的。除了新的方法外，我们还通过建立参数系数估计量的根n一致性和渐近正态性以及神经非参数函数估计量的最小最大最优收敛速率为所提出的模型提供了理论证明。通过几个模拟和真实数据示例，所提出的模型在经验上比各种替代方法产生更好的估计和更准确的预测。
Abstract Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regression remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more parsimonious way than nonparametric smoothing methods. However, while deep learning brought breakthroughs in prediction, it is not well suited for statistical inference due to its black box nature. In this article, we leverage the advantages of deep learning and apply it to quantile regression where the goal is to produce interpretable results and perform statistical inference. We achieve this by adopting a semiparametric approach based on the partially linear quantile regression model, where covariates of primary interest for statistical inference are modeled linearly and all other covariates are modeled nonparametrically by means of a deep neural network. In addition to the new methodology, we provide theoretical justification for the proposed model by establishing the root-n consistency and asymptotically normality of the parametric coefficient estimator and the minimax optimal convergence rate of the neural nonparametric function estimator. Across several simulated and real data examples, the proposed model empirically produces superior estimates and more accurate predictions than various alternative approaches.