ON THE DISTRIBUTION OF TAIL ARRAY SUMS FOR STRONGLY MIXING STATIONARY-SEQUENCES

This paper concerns the asymptotic distributions of ''tail array'' sum s of the form Sigma psi(n)(X-i - u(n)) where {X-i} is a strongly mixin g stationary sequence, psi(n) are real functions which are constant fo r negative arguments, psi(n)(x) = psi(n)(X+) and {u(n)} are levels wit h u(n) --> infinity. Compound Poisson limits for rapid convergence of u(n) --> infinity (nP{X-1 > u(n)} --> tau < infinity) are considered b riefly and a more detailed account given for normal limits applicable to slower rates (nP(X-1 > u(n)) --> infinity). The work is motivated b y (1) the modeling of ''damage'' due to very high and moderately high extremes and (2) the provision of probabilistic theory for application to problems of ''tail inference'' for stationary sequences.