Fast Calibrated Additive Quantile Regression

• 成果类型: Article
• 署名作者: Fasiolo, Matteo; Wood, Simon N.; Zaffran, Margaux; Nedellec, Raphael; Goude, Yannig
• 署名单位: University of Bristol; Institut Polytechnique de Paris; ENSTA Paris; Electricite de France (EDF)
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1725521
• 发表日期: 2021
• 页码: 1402-1412
• 关键词: smoothing parameter; distributions; selection

摘要

We propose a novel framework for fitting additive quantile regression models, which provides well-calibrated inference about the conditional quantiles and fast automatic estimation of the smoothing parameters, for model structures as diverse as those usable with distributional generalized additive models, while maintaining equivalent numerical efficiency and stability. The proposed methods are at once statistically rigorous and computationally efficient, because they are based on the general belief updating framework of Bissiri, Holmes, and Walker to loss based inference, but compute by adapting the stable fitting methods of Wood, Pya, and Safken. We show how the pinball loss is statistically suboptimal relative to a novel smooth generalization, which also gives access to fast estimation methods. Further, we provide a novel calibration method for efficiently selecting the learning rate balancing the loss with the smoothing priors during inference, thereby obtaining reliable quantile uncertainty estimates. Our work was motivated by a probabilistic electricity load forecasting application, used here to demonstrate the proposed approach. The methods described here are implemented by the qgam R package, available on the Comprehensive R Archive Network (CRAN). for this article are available online.