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LASSO-type penalization in the framework of generalized additive models for location, scale and shape

Author

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  • Groll, Andreas
  • Hambuckers, Julien
  • Kneib, Thomas
  • Umlauf, Nikolaus

Abstract

For numerous applications, it is of interest to provide full probabilistic forecasts, which are able to assign plausibilities to each predicted outcome. Therefore, attention is shifting constantly from conditional mean models to probabilistic distributional models capturing location, scale, shape and other aspects of the response distribution. One of the most established models for distributional regression is the generalized additive model for location, scale and shape (GAMLSS). In high-dimensional data set-ups, classical fitting procedures for GAMLSS often become rather unstable and methods for variable selection are desirable. Therefore, a regularization approach for high-dimensional data set-ups in the framework of GAMLSS is proposed. It is designed for linear covariate effects and is based on L1-type penalties. The following three penalization options are provided: the conventional least absolute shrinkage and selection operator (LASSO) for metric covariates, and both group and fused LASSO for categorical predictors. The methods are investigated both for simulated data and for two real data examples, namely Munich rent data and data on extreme operational losses from the Italian bank UniCredit.

Suggested Citation

  • Groll, Andreas & Hambuckers, Julien & Kneib, Thomas & Umlauf, Nikolaus, 2019. "LASSO-type penalization in the framework of generalized additive models for location, scale and shape," Computational Statistics & Data Analysis, Elsevier, vol. 140(C), pages 59-73.
    • Handle: RePEc:eee:csdana:v:140:y:2019:i:c:p:59-73
    DOI: 10.1016/j.csda.2019.06.005
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    Cited by:

    1. Barbagli, Matteo & François, Pascal & Gauthier, Geneviève & Vrins, Frédéric, 2025. "The role of CDS spreads in explaining bond recovery rates," Journal of Banking & Finance, Elsevier, vol. 174(C).
    2. Simon Hirsch & Jonathan Berrisch & Florian Ziel, 2024. "Online Distributional Regression," Papers 2407.08750, arXiv.org, revised Aug 2025.
    3. Hendrik van der Wurp & Andreas Groll, 2023. "Introducing LASSO-type penalisation to generalised joint regression modelling for count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 127-151, March.
    4. Kneib, Thomas & Silbersdorff, Alexander & Säfken, Benjamin, 2023. "Rage Against the Mean – A Review of Distributional Regression Approaches," Econometrics and Statistics, Elsevier, vol. 26(C), pages 99-123.
    5. Simon Hirsch, 2025. "Online Multivariate Regularized Distributional Regression for High-dimensional Probabilistic Electricity Price Forecasting," Papers 2504.02518, arXiv.org, revised Oct 2025.
    6. Marco Bee & Julien Hambuckers & Flavio Santi & Luca Trapin, 2021. "Testing a parameter restriction on the boundary for the g-and-h distribution: a simulated approach," Computational Statistics, Springer, vol. 36(3), pages 2177-2200, September.
    7. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    8. Linda Mhalla & Julien Hambuckers & Marie Lambert, 2022. "Extremal connectedness of hedge funds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 988-1009, August.
    9. Paul F. V. Wiemann & Thomas Kneib & Julien Hambuckers, 2024. "Using the softplus function to construct alternative link functions in generalized linear models and beyond," Statistical Papers, Springer, vol. 65(5), pages 3155-3180, July.
    10. Muschinski, Thomas & Mayr, Georg J. & Simon, Thorsten & Umlauf, Nikolaus & Zeileis, Achim, 2024. "Cholesky-based multivariate Gaussian regression," Econometrics and Statistics, Elsevier, vol. 29(C), pages 261-281.
    11. Amon, Julian & Hornik, Kurt, 2022. "Is it all bafflegab? – Linguistic and meta characteristics of research articles in prestigious economics journals," Journal of Informetrics, Elsevier, vol. 16(2).

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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