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The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis

Author

Listed:
  • Villani, Mattias

    (Research Department, Central Bank of Sweden)

  • Larsson, Rolf

    (Department of Information Science, Uppsala University)

Abstract

The multivariate split nomal distribution extends the usual multivariate normal distribution by a set of parameters which allows for skewness in the form of contraction/dilation along a subset of the prinicpal axis. The paper derives some properties for this distribution, including its moment generating function, multivariate skewness and kurtosis. Maximum likelihood estimation is discussed and a complete Bayesian analysis of the multivariate split normal distribution is developed.

Suggested Citation

  • Villani, Mattias & Larsson, Rolf, 2004. "The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis," Working Paper Series 175, Sveriges Riksbank (Central Bank of Sweden).
    • Handle: RePEc:hhs:rbnkwp:0175
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    File URL: http://www.riksbank.com/upload/WorkingPapers/WP_175.pdf
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    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
    3. Blix, Mårten & Sellin, Peter, 2000. "A Bivariate Distribution for Inflation and Output Forecasts," Working Paper Series 102, Sveriges Riksbank (Central Bank of Sweden).
    4. Kadane, Joseph B. & Chan, Ngai Hang & Wolfson, Lara J., 1996. "Priors for unit root models," Journal of Econometrics, Elsevier, vol. 75(1), pages 99-111, November.
    5. John Geweke, 1999. "Using Simulation Methods for Bayesian Econometric Models," Computing in Economics and Finance 1999 832, Society for Computational Economics.
    6. Luc Bauwens & Winfried Pohlmeier & David Veredas, 2006. "Editor’s introduction," Empirical Economics, Springer, vol. 30(4), pages 791-794, January.
    7. Bauwens, Luc & Polasek, Wolfgang & van Dijk, Herman K., 1996. "Editor's introduction," Journal of Econometrics, Elsevier, vol. 75(1), pages 1-5, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Maximiano Pinheiro & Paulo Esteves, 2012. "On the uncertainty and risks of macroeconomic forecasts: combining judgements with sample and model information," Empirical Economics, Springer, vol. 42(3), pages 639-665, June.
    2. Maximiano Pinheiro, 2012. "Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables," Journal of Probability and Statistics, Hindawi, vol. 2012, pages 1-10, April.

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    More about this item

    Keywords

    Bayesian inference; Elicitation; Estimation; Maximum likelihood; Multivariate analysis; Skewness;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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