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Multivariate reduced rank regression in non-Gaussian contexts, using copulas

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  • HEINEN, Andréas
  • RENGIFO, Erick

Abstract

We propose a new procedure to perform Reduced Rank Regression (RRR) in nonGaussian contexts, based on Multivariate Dispersion Models. Reduced-Rank Multivariate Dispersion Models (RR-MDM) generalise RRR to a very large class of distributions, which include continuous distributions like the normal, Gamma, Inverse Gaussian, and discrete distributions like the Poisson and the binomial. A multivariate distribution is created with the help of the Gaussian copula and estimation is performed using maximum likelihood. We show how this method can be amended to deal with the case of discrete data. We perform Monte Carlo simulations and show that our estimator is more efficient than the traditional Gaussian RRR. In the framework of MDM's we introduce a procedure analogous to canonical correlations, which takes into account the distribution of the data.

Suggested Citation

  • HEINEN, Andréas & RENGIFO, Erick, 2004. "Multivariate reduced rank regression in non-Gaussian contexts, using copulas," LIDAM Discussion Papers CORE 2004032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2004032
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    References listed on IDEAS

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    1. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
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    10. Heinen, Andreas & Rengifo, Erick, 2007. "Multivariate autoregressive modeling of time series count data using copulas," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 564-583, September.
    11. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
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    Cited by:

    1. Mike Vuolo, 2017. "Copula Models for Sociology: Measures of Dependence and Probabilities for Joint Distributions," Sociological Methods & Research, , vol. 46(3), pages 604-648, August.
    2. Yee, Thomas W., 2014. "Reduced-rank vector generalized linear models with two linear predictors," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 889-902.
    3. Ben Omrane, Walid & Heinen, Andréas, 2010. "Public news announcements and quoting activity in the Euro/Dollar foreign exchange market," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2419-2431, November.

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    More about this item

    Keywords

    multivariate dispersion model; multivariate statistical analysis; canonical correlations; principal component analsysis;
    All these keywords.

    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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