Fast Calibrated Additive Quantile Regression
| Autor: | Simon N. Wood, Matteo Fasiolo, Raphael Nedellec, Yannig Goude, Margaux Zaffran |
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| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Statistics::Theory Inference Statistics - Applications Statistics - Computation 01 natural sciences Methodology (stat.ME) 010104 statistics & probability 0502 economics and business Statistics Statistics::Methodology Applications (stat.AP) 0101 mathematics Computation (stat.CO) Statistics - Methodology 050205 econometrics Mathematics Statistics::Applications 05 social sciences Generalized additive model Statistics::Computation Quantile regression Statistics Probability and Uncertainty Smoothing Quantile |
| Zdroj: | Journal of the American Statistical Association. 116:1402-1412 |
| ISSN: | 1537-274X 0162-1459 |
| DOI: | 10.1080/01621459.2020.1725521 |
| Popis: | 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 rigorous and 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 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 demonstrate the proposed approach. The methods described here are implemented by the qgam R package, available on the Comprehensive R Archive Network (CRAN). |
| Databáze: | OpenAIRE |
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