Simultaneous estimation of large numbers of extreme quantiles in simulation experiments

Abstract

The large random access memory and high internal speeds of present day computers can be used to increase the efficiency of large-scale simulation experiments by estimating simultaneously several quantiles of each of several statistics. In order to do this without inordinately increasing programming complexity, quantile estimation schemes are required which are simple and do not depend on special features of the distributions of the statistics considered. The author discusses limitations, when the probability level alpha is very high or very low, of two basic methods of estimating quantiles. One method is the direct use of order statistics; the other is based on the use of stochastic approximation. Several modifications of these two estimation schemes are considered. In particular a simple and computationally efficient transformation of the simulation data is proposed and the properties (i.e. bias and variance) of quantile estimates based on this scheme are discussed