A LARGE-SAMPLE TEST FOR ONE-PARAMETER FAMILIES OF COPULAS

This paper presents a large sample test of the hypothesis that the copula of a bivariate distribution belongs to a family of copulas parametrized by Spearman's correlation such as the family of Morgenstern copulas. The test statistic is based on the fact that if a copula belongs to the family then Kendall's tau may be expressed as a function of Spearman's rho. Using this relationship along with U-statistic estimators of tau and rho, we construct a test statistic that is asymptotically normal. To simplify calculations we suggest that the variance be estimated with a jackknife estimator.