Fast Calibrated Additive Quantile Regression
提出一种加性分位数回归框架，能自动估计平滑参数并提供校准的分位数推断，计算效率与稳定性与分布GAM相当，基于信念更新框架并适配稳定拟合方法，通过新平滑损失函数和校准方法提升统计性能，在电力负荷预测中验证。
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 GAMs, while maintaining equivalent numerical efficiency and stability. The proposed methods are at once statistically rigorousand computationally efficient, because they are based on the general belief updating framework of Bissiri et al. (2016) to loss based inference, but compute by adapting<br/>the stable fitting methods of Wood et al. (2016). We show how the pinball loss is statistically suboptimal relative to a novel smooth generalisation, 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<br/>demonstrate the proposed approach. The methods described here are implemented by the qgam R package, available on the Comprehensive R Archive Network (CRAN).