Limiting distributions of maxima under triangular schemes

A well-known result in extreme value theory indicates that componentwise taken sample maxima of random vectors are asymptotically independent under weak conditions. However, in important cases this independence is attained at a very slow rate so that the residual dependence structure plays a significant role. In the present article, we deduce limiting distributions of maxima under triangular schemes of random vectors. The residual dependence is expressed by a technical condition imposed on the spectral expansion of the underlying distribution.