Fast Calibrated Additive Quantile Regression

We propose a novel framework for fitting additive quantile regression models,which provides well calibrated inference about the conditional quantiles and fastautomatic estimation of the smoothing parameters, for model structures as diverseas those usable with distributional GAMs, while maintaining equivalent numericalefficiency and stability. The proposed methods are at once statistically rigorousand computationally efficient, because they are based on the general belief updatingframework of Bissiri et al. (2016) to loss based inference, but compute by adaptingthe stable fitting methods of Wood et al. (2016). We show how the pinball loss isstatistically suboptimal relative to a novel smooth generalisation, which also givesaccess to fast estimation methods. Further, we provide a novel calibration methodfor efficiently selecting the ‘learning rate’ balancing the loss with the smoothing priorsduring inference, thereby obtaining reliable quantile uncertainty estimates. Our workwas motivated by a probabilistic electricity load forecasting application, used here todemonstrate the proposed approach. The methods described here are implementedby the qgam R package, available on the Comprehensive R Archive Network (CRAN).