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Semiparametric estimation of the dependence parameter of the error terms in multivariate regression


Author Info

  • Gunky Kim


  • Mervyn J. Silvapulle


  • Paramsothy Silvapulle



A semiparametric method is developed for estimating the dependence parameter and the joint distribution of the error term in the multivariate linear regression model. The nonparametric part of the method treats the marginal distributions of the error term as unknown, and estimates them by suitable empirical distribution functions. Then a pseudolikelihood is maximized to estimate the dependence parameter. It is shown that this estimator is asymptotically normal, and a consistent estimator of its large sample variance is given. A simulation study shows that the proposed semiparametric estimator is better than the parametric methods available when the error distribution is unknown, which is almost always the case in practice. It turns out that there is no loss of asymptotic efficiency due to the estimation of the regression parameters. An empirical example on portfolio management is used to illustrate the method. This is an extension of earlier work by Oakes (1994) and Genest et al. (1995) for the case when the observations are independent and identically distributed, and Oakes and Ritz (2000) for the multivariate regression model.

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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 1/07.

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Length: 29 pages
Date of creation: Feb 2007
Date of revision:
Handle: RePEc:msh:ebswps:2007-1

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Keywords: Copula; Pseudo-likelihood; Robustness.;

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  1. Weijing Wang, 2003. "Estimating the association parameter for copula models under dependent censoring," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 257-273.
  2. Karen Bandeen-Roche, 2002. "Modelling multivariate failure time associations in the presence of a competing risk," Biometrika, Biometrika Trust, vol. 89(2), pages 299-314, June.
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