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Efficient Estimation of Semiparametric Multivariate Copula Models

  • Chen, Xiaohong
  • Fan, Yanqin
  • Tsyrennikov, Viktor

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.

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Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 101 (2006)
Issue (Month): (September)
Pages: 1228-1240

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Handle: RePEc:bes:jnlasa:v:101:y:2006:p:1228-1240
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  1. Gallant, A Ronald & Nychka, Douglas W, 1987. "Semi-nonparametric Maximum Likelihood Estimation," Econometrica, Econometric Society, vol. 55(2), pages 363-90, March.
  2. Coppejans, Mark & Gallant, A. Ronald, 2000. "Cross Validated SNP Density Estimates," Working Papers 00-10, Duke University, Department of Economics.
  3. Granger, Clive W.J. & Teräsvirta, Timo & Patton, Andrew J, 2002. "Common Factors in Conditional Distributions," University of California at San Diego, Economics Working Paper Series qt3bd1n1x5, Department of Economics, UC San Diego.
  4. Lee, Lung-Fei, 1982. "Some Approaches to the Correction of Selectivity Bias," Review of Economic Studies, Wiley Blackwell, vol. 49(3), pages 355-72, July.
  5. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  6. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 130-168.
  7. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  8. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-12, March.
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