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Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression

Author

Listed:
  • Yuanhua Feng

    (Paderborn University)

  • Wolfgang Karl Härdle

    (Humboldt University Berlin)

Abstract

This paper introduces first an extended SAN (sinh-arcsinh normal) family of distri- butions by allowing the transformed normal random variable to be unstandardized. A Log-SAN transformation for non-negative random variables and the associate Log-SAN family of distributions are then proposed. Properties of those distribu- tions are investigated. A maximum likelihood estimation procedure is proposed. A chain mixed multivariate extension of the SAN distributions and a corresponding distributional regression model are then defined. Those approaches can help us to discover possible spurious or hidden bimodal property of a multivariate distribution. The proposals are illustrated by different examples.

Suggested Citation

  • Yuanhua Feng & Wolfgang Karl Härdle, 2021. "Uni- and multivariate extensions of the sinh-arcsinh normal distribution applied to distributional regression," Working Papers CIE 142, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:142
    as

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    File URL: http://groups.uni-paderborn.de/wp-wiwi/RePEc/pdf/ciepap/WP142.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Extended SAS distribution; Log-SAS distribution; MLE; chain mixed multivariate distribution; distributional regression; spurious and hidden bimodality;
    All these keywords.

    JEL classification:

    • 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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