Efficient Estimation of Some Elliptical Copula Regression Models through Scale Mixtures of Normal

We simplify the implementation of some elliptical copula regression models through the normal representation. Both copula and marginal probability density functions are expressed as the scale mixtures of normals to facilitate the estimation procedure. With the fact that all elliptical distributions have the same correlation structure and some of them can be expressed as a scale mixture of multivariate normal, we can then estimate their correlation matrix with ease. Two simulation studies are illustrated to assess the performance of our proposed models and methods. We also conduct two empirical studies on U.S. excess return and Thai wage earnings to show the applicability to the multivariate Capital Asset Pricing Model and the bivariate seemingly unrelated Tobit model, respectively.