Large Quantile Estimation in a Multivariate Setting

An asymptotic theory is developed for the estimation of high quantile curves, i.e., sets of points in higher dimensional space for which the exeedance probability is pn, with npn → 0 (n → ∞). Here n is the number of available observations. This is the situation of interest if one wants to protect against a calamity that has not yet occurred. Asymptotic normality of the estimated quantile curve is proved under appropriate conditions, including the domain of the attraction condition for multivariate extremes.