Nonparametric quantile estimation using importance sampling

摘要

Nonparametric estimation of a quantile of a random variable m(X) is considered, where is a function which is costly to compute and X is a -valued random variable with a given density. An importance sampling quantile estimate of m(X), which is based on a suitable estimate of m, is defined, and it is shown that this estimate achieves a rate of convergence of order . The finite sample size behavior of the estimate is illustrated by simulated data.