Estimation Methods for Nonhomogeneous Regression Models: Minimum Continuous Ranked Probability Score versus Maximum Likelihood

By Manuel Gebetsberger, Jakob W. Messner, Georg J. Mayr, Achim Zeileis. Monthly Weather Review, 2018

51 citations recorded by the source corpus.

Nonhomogeneous regression models are widely used to statistically postprocess numerical ensemble weather prediction models. Such regression models are capable of forecasting full probability distributions and correcting for ensemble errors in the mean and variance. To estimate the corresponding regression coefficients, minimization of the continuous ranked probability score (CRPS) has widely been used in meteorological postprocessing studies and has often been found to yield more calibrated forecasts compared to maximum likelihood estimation. From a theoretical perspective, both estimators are consistent and should lead to similar results, provided the correct distribution assumption about empirical data. Differences between the estimated values indicate a wrong specification of the regression model. This study compares the two estimators for probabilistic temperature forecasting with nonhomogeneous regression, where results show discrepancies for the classical Gaussian assumption. The heavy-tailed logistic and Student’s t distributions can improve forecast performance in terms of sharpness and calibration, and lead to only minor differences between the estimators employed. Finally, a simulation study confirms the importance of appropriate distribution assumptions and shows that for a correctly specified model the maximum likelihood estimator is slightly more efficient than the CRPS estimator.

Subfields: Artificial Intelligence, Atmospheric Science, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/073d7c255b4ae3718120a113f51d159d9947019b

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Citations in the corpus

NGBoost: Natural Gradient Boosting for Probabilistic Prediction (2019, background): “We present Natural Gradient Boosting, a modular algorithm for probabilistic regression (section 3.4) which uses multiparameter boosting and natural gradients to integrate any choice of: • Base learner (e.g. Regression Tree), • Parametric probability distribution (Normal, Laplace, etc.), and • Scorin”