• ORDER STATISTICS, LORENZ TRANSFORM AND THE CVAR RISK MEASURE

Abstract

The class of linear functions of order statistics or L-estimates is considered. Under finite variances and other suitable restrictions, it is known that L-estimates converge in distribution to a normal distribution as the sample size increases to infinity. This result is applied to obtain approximate confidence intervals for the Lorenz transform and the conditional value-at-risk measure using L-estimates in case the data follows an approximate generalised Pareto distribution with finite variance. By infinite variance, the goodness-of-fit of the L-estimate compared to the true Lorenz transform is measured using the expected relative error of approximation.