  The multivariate extremal index function relates the asymptotic distribution
of the vector of pointwise maxima of a multivariate stationary sequence to that
of the independent sequence from the same stationary distribution. It also
measures the degree of clustering of extremes in the multivariate process. In
this paper, we construct nonparametric estimators of this function and prove
their asymptotic normality under long-range dependence and moment conditions.
The results are illustrated by means of a simulation study.
