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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, University of Innsbruck.
  • Handle: RePEc:inn:wpaper:2018-16
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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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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