A NONPARAMETRIC-ESTIMATION PROCEDURE FOR BIVARIATE EXTREME-VALUE COPULAS

A bivariate extreme value distribution with fixed marginals is generat ed by a one-dimensional map called a dependence function. This paper p roposes a new nonparametric estimator of this function. Its asymptotic properties are examined, and its small-sample behaviour is compared t o that of other rank-based and likelihood-based procedures. The new es timator is shown to be uniformly, strongly convergent and asymptotical ly unbiased. Through simulations, it is also seen to perform reasonabl y well against the maximum likelihood estimator based on the correct m odel and to have smaller L-1, L-2 and L-infinity errors than any exist ing nonparametric alternative. The n(1/2) consistency of the proposed estimator leads to nonparametric estimation of Tawn's (1988) dependenc e measure that may be used to test independence in small samples.