Estimation methods for non-homogeneous regression models: Minimum continuous ranked probability score vs. maximum likelihood

Manuel Gebetsberger*, Jakob W. Messner, Georg J. Mayr, Achim Zeileis

*Corresponding author for this work

    Research output: Contribution to journalJournal articleResearchpeer-review

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    Abstract

    Non-homogeneous regression models are widely used to statistically postprocess
    numerical ensemble weather prediction models. Such regression
    models are capable of forecasting full probability distributions and correct
    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 post-processing 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 non-homogeneous regression, where results show discrepancies for the
    classical Gaussian assumption. The heavy-tailed logistic and Student-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.
    KEYWORDS: ensemble post-processing, maximum likelihood, CRPS minimization,
    probabilistic forecasting, distributional regression models
    Original languageEnglish
    JournalMonthly Weather Review
    Volume146
    Issue number12
    Pages (from-to)4323-4338
    Number of pages16
    ISSN0027-0644
    DOIs
    Publication statusPublished - 2018

    Bibliographical note

    This article is licensed under a Creative Commons Attribution 4.0 license (http://creativecommons.org/licenses/by/4.0/).

    Keywords

    • Ensemble post-processing
    • Maximum likelihood
    • CRPS minimization
    • Probabilistic forecasting
    • distributional regression models

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