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

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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.

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  • 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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    1. 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.
    2. Barbagli, Matteo & François, Pascal & Gauthier, Geneviève & Vrins, Frédéric, 2024. "The role of CDS spreads in explaining bond recovery rates," LIDAM Discussion Papers LFIN 2024002, Université catholique de Louvain, Louvain Finance (LFIN).
    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. 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.
    5. 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.
    6. 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.
    7. 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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    More about this item

    Keywords

    GAMLSS; Distributional regression; Model selection; LASSO; Fused LASSO;
    All these keywords.

    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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