A study on asymptotically unbiased estimators of an FGM copula

摘要

A copula, one of the multivariate distributions, is known as a useful tool for dependence modeling because they can express high and non-linear correlations of random variables. Thus, parameter estimation for copulas is effective in analyzing dependence structures among data. However, it is computationally hard work because copulas have many parameters such as marginal parameters and dependence parameters in general. For example, ad-variate Farlie-Gumbel-Morgenstern (FGM) copula has 2~d - d - 1 dependence parameters, and therefore the ordinary maximum likelihood estimation (MLE) is not practical from the viewpoint of the computational complexity. In this study, we present a computable estimation method for the FGM copula by using the theory of inference functions for margins. Moreover, we prove that the estimator holds asymptotic unbiasedness.