Efficient Estimation of Semiparametric Multivariate Copula Models
AbstractWe 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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Bibliographic InfoPaper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0420.
Date of creation: Sep 2004
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Web page: http://www.vanderbilt.edu/econ/wparchive/index.html
Multivariate copula; sieve maximum likelihood; semiparametric efficiency;
Other versions of this item:
- Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006. "Efficient Estimation of Semiparametric Multivariate Copula Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1228-1240, September.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-12-12 (All new papers)
- NEP-ECM-2004-12-12 (Econometrics)
- NEP-FIN-2004-12-12 (Finance)
- NEP-FIN-2004-12-15 (Finance)
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