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Modeling Conditional Densities Using Finite Smooth Mixtures

Author

Listed:
  • Li, Feng

    (Department of Statistics)

  • Villani, Mattias

    (Research Department, Central Bank of Sweden)

  • Kohn, Robert

    (The University of New South Wales)

Abstract
Smooth mixtures, i.e. mixture models with covariate-dependent mixing weights, are very useful flexible models for conditional densities. Previous work shows that using too simple mixture components for modeling heteroscedastic and/or heavy tailed data can give a poor fit, even with a large number of components. This paper explores how well a smooth mixture of symmetric components can capture skewed data. Simulations and applications on real data show that including covariate-dependent skewness in the components can lead to substantially improved performance on skewed data, often using a much smaller number of components. Furthermore, variable selection is effective in removing unnecessary covariates in the skewness, which means that there is little loss in allowing for skewness in the components when the data are actually symmetric. We also introduce smooth mixtures of gamma and log-normal components to model positively-valued response variables.

Suggested Citation

  • Li, Feng & Villani, Mattias & Kohn, Robert, 2010. "Modeling Conditional Densities Using Finite Smooth Mixtures," Working Paper Series 245, Sveriges Riksbank (Central Bank of Sweden).
    • Handle: RePEc:hhs:rbnkwp:0245
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    File URL: http://www.riksbank.com/upload/Dokument_riksbank/Kat_publicerat/WorkingPapers/2010/wp245.pdf
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    Citations

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    Cited by:

    1. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    2. Almeida e Santos Nogueira, R.J. & Basturk, N. & Kaymak, U. & Costa Sousa, J.M., 2013. "Estimation of flexible fuzzy GARCH models for conditional density estimation," ERIM Report Series Research in Management ERS-2013-013-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    3. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    4. Yanfei Kang & Rob J Hyndman & Feng Li, 2018. "Efficient generation of time series with diverse and controllable characteristics," Monash Econometrics and Business Statistics Working Papers 15/18, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    Bayesian inference; Markov chain Monte Carlo; Mixture of Experts; Variable selection;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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