  We propose a new class of estimators for Pickands dependence function which
is based on the concept of minimum distance estimation. An explicit integral
representation of the function $A^*(t)$, which minimizes a weighted
$L^2$-distance between the logarithm of the copula $C(y^{1-t},y^t)$ and
functions of the form $A(t)\log(y)$ is derived. If the unknown copula is an
extreme-value copula, the function $A^*(t)$ coincides with Pickands dependence
function. Moreover, even if this is not the case, the function $A^*(t)$ always
satisfies the boundary conditions of a Pickands dependence function. The
estimators are obtained by replacing the unknown copula by its empirical
counterpart and weak convergence of the corresponding process is shown. A
comparison with the commonly used estimators is performed from a theoretical
point of view and by means of a simulation study. Our asymptotic and numerical
results indicate that some of the new estimators outperform the estimators,
which were recently proposed by Genest and Segers [Ann. Statist. 37 (2009)
2990--3022]. As a by-product of our results, we obtain a simple test for the
hypothesis of an extreme-value copula, which is consistent against all positive
quadrant dependent alternatives satisfying weak differentiability assumptions
of first order.
