A stochastic approximation algorithm for quantile estimation

Abstract

In this paper, we present two new stochastic approximation algorithms for the problem of quantile estimation. The algorithms uses the characterization of the quantile provided in terms of an optimization problem in [1]. The algorithms take the shape of a stochastic gradient descent which minimizes the optimization problem. Asymptotic convergence of the algorithms to the true quantile is proven using the ODE method. The theoretical results are also supplemented through empirical evidence. The algorithms are shown to provide significant improvement in terms of memory requirement and accuracy.