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Multivariate Method Of Simulated Quantiles

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Listed:
  • Paola Stolfi
  • Mauro Bernardi
  • Lea Petrella

Abstract

In this paper the Method of Simulated Quantiles (MSQ) of Dominicy and Veredas (2013) is extended to a multivariate framework by introducing the Multivariate Method of Simulated Quantiles (MMSQ). In order to build the MMSQ procedure we rely on the definition of projectional quantile which allows us to estimate in the optimal way all the parameters involved in the multivariate setting. We provide asymptotic results underlying the MMSQ estimator. As a further improvement we introduce a penalty function in the procedure in order to account for sparsity by using the Smoothly Clipped Absolute Deviation function. Oracle properties are showed for the penalized MMSQ estimators while simulation results are considered to highlight the power of the inferential procedure.

Suggested Citation

  • Paola Stolfi & Mauro Bernardi & Lea Petrella, 2016. "Multivariate Method Of Simulated Quantiles," Departmental Working Papers of Economics - University 'Roma Tre' 0212, Department of Economics - University Roma Tre.
    • Handle: RePEc:rtr:wpaper:0212
    as

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    File URL: http://dipeco.uniroma3.it/db/docs/WP%20212(1).pdf
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    References listed on IDEAS

    as
    1. Paindaveine, Davy & Siman, Miroslav, 2011. "On directional multiple-output quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 193-212, February.
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    3. Yves Dominicy & Hiroaki Ogata & David Veredas, 2013. "Inference for vast dimensional elliptical distributions," Computational Statistics, Springer, vol. 28(4), pages 1853-1880, August.
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    5. Jacob Bien & Robert J. Tibshirani, 2011. "Sparse estimation of a covariance matrix," Biometrika, Biometrika Trust, vol. 98(4), pages 807-820.
    6. Marc Hallin & Davy Paindaveine & Miroslav Siman, 2008. "Multivariate quantiles and multiple-output regression quantiles: from L1 optimization to halfspace depth," Working Papers ECARES 2008_042, ULB -- Universite Libre de Bruxelles.
    7. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    8. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    directional quantiles; method of simulated quantiles; quantile matching; sparsity.;
    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
    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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