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LASSO-Type Penalization in the Framework of Generalized Additive Models for Location, Scale and Shape

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

Abstract

For numerous applications it is of interest to provide full probabilistic forecasts, which are able to assign probabilities 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 the GAMLSS often become rather unstable and methods for variable selection are desirable. Therefore, we propose a regularization approach for high dimensional data set-ups in the framework for GAMLSS. 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

  • Andreas Groll & Julien Hambuckers & Thomas Kneib & Nikolaus Umlauf, 2018. "LASSO-Type Penalization in the Framework of Generalized Additive Models for Location, Scale and Shape," Working Papers 2018-16, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2018-16
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    References listed on IDEAS

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    1. Julien Hambuckers & Andreas Groll & Thomas Kneib, 2018. "Understanding the economic determinants of the severity of operational losses: A regularized generalized Pareto regression approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 898-935, September.
    2. Thomas Kneib & Susanne Konrath & Ludwig Fahrmeir, 2011. "High dimensional structured additive regression models: Bayesian regularization, smoothing and predictive performance," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(1), pages 51-70, January.
    3. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    4. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    5. Nikolaus Umlauf & Nadja Klein & Achim Zeileis, 2017. "BAMLSS: Bayesian Additive Models for Location, Scale and Shape (and Beyond)," Working Papers 2017-05, Faculty of Economics and Statistics, Universität Innsbruck.
    6. Chapelle, Ariane & Crama, Yves & Hübner, Georges & Peters, Jean-Philippe, 2008. "Practical methods for measuring and managing operational risk in the financial sector: A clinical study," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1049-1061, June.
    7. Andreas Mayr & Nora Fenske & Benjamin Hofner & Thomas Kneib & Matthias Schmid, 2012. "Generalized additive models for location, scale and shape for high dimensional data—a flexible approach based on boosting," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(3), pages 403-427, May.
    8. Howard D. Bondell & Brian J. Reich, 2009. "Simultaneous Factor Selection and Collapsing Levels in ANOVA," Biometrics, The International Biometric Society, vol. 65(1), pages 169-177, March.
    9. Valérie Chavez-Demoulin & Paul Embrechts & Marius Hofert, 2016. "An Extreme Value Approach for Modeling Operational Risk Losses Depending on Covariates," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(3), pages 735-776, September.
    10. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    11. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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. 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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