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Efficient Estimation of Semiparametric Multivariate Copula Models

Author

Listed:
  • Xiaohong Chen

    () (Department of Economics, New York University)

  • Yanqin Fan

    () (Department of Economics, Vanderbilt University)

  • Victor Tsyrennifov

    () (Department of Economics, New York University)

Abstract

We propose a sieve maximum likelihood (ML) estimation procedure for a broad class of semiparametric multivariate distribution models. A joint distribution in this class is characterized by a parametric copula function evaluated at nonparametric marginal distributions. This class of models has gained popularity in diverse fields due to a) its flexibility in separately modeling the dependence structure and the marginal behaviors of a multivariate random variable, and b) its circumvention of the "curse of dimensionality" associated with purely nonparametric multivariate distributions. We show that the plug-in sieve ML estimates of all smooth functionals, including the finite dimensional copula parameters and the unknown marginal distributions, are semiparametrically efficient; and that their asymptotic variances can be estimated consistently. Moreover, prior restrictions on the marginal distributions can be easily incorporated into the sieve ML procedure to achieve further efficiency gains. Two such cases are studied in the paper: (i) the marginal distributions are equal but otherwise unspecifed, and (ii) some but not all marginal distributions are parametric. Monte Carlo studies indicate that the sieve ML estimates perform well in finite samples, especially so when prior information on the marginal distributions is incorporated.

Suggested Citation

  • Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
  • Handle: RePEc:van:wpaper:0420
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    References listed on IDEAS

    as
    1. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-390, March.
    2. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    3. Coppejans, Mark & Gallant, A. Ronald, 2002. "Cross-validated SNP density estimates," Journal of Econometrics, Elsevier, vol. 110(1), pages 27-65, September.
    4. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    5. Granger, Clive W.J. & Terasvirta, Timo & Patton, Andrew J., 2006. "Common factors in conditional distributions for bivariate time series," Journal of Econometrics, Elsevier, vol. 132(1), pages 43-57, May.
    6. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    7. Lung-Fei Lee, 1982. "Some Approaches to the Correction of Selectivity Bias," Review of Economic Studies, Oxford University Press, vol. 49(3), pages 355-372.
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    More about this item

    Keywords

    Multivariate copula; sieve maximum likelihood; semiparametric efficiency;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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