Abstract: This study considers the problem of estimating a time-dependent quantile at each time point t ϵ [0, 1], given independent samples of a stochastic process at discrete time points in [0, 1]. It is assumed that the quantiles depend smoothly on t. Here we present the rate of convergence of quantile estimates based on a local average estimate of the time-dependent cumulative distribution functions. Then we apply importance sampling in a simulation model to construct estimates that achieve better rates of convergence. Lastly, we demonstrate the finite-sample performance of our estimates by applying them to simulated data.

Key words and phrases: Conditional quantile estimation, importance sampling, rate of convergence.