Quantile Estimation Based on the Principles of the Search on the Line

Abstract

The goal of our research is to estimate the quantiles of a distribution from a large set of samples that arrive sequentially. We propose a novel quantile estimator that requires a finite memory and is simple to implement. Furthermore, the estimator falls under the family of incremental estimators, i.e., it utilizes the previously-computed estimates and only resorts to the last sample for updating these estimates. The estimator estimates the quantile on a set of discrete values. Choosing a low resolution results in fast convergence and low precision of the current estimate after convergence, while a high resolution results in slower convergence, but higher precision. The convergence results are based on the theory of Stochastic Point Location (SPL). The reader should note that the aim of the paper is to demonstrate its salient properties as a novel quantile estimator that uses only finite memory.