One-dimensional quantile-stratified sampling and its application in statistical simulations

TL;DR

This paper explores a novel one-dimensional quantile-stratified sampling method, analyzing its properties and comparing its effectiveness to standard IID sampling and importance sampling in statistical simulations.

Contribution

It introduces and evaluates a new quantile-stratified sampling technique, highlighting its advantages over traditional sampling methods in importance sampling applications.

Findings

Quantile-stratified sampling differs from IID sampling in key properties.

The method improves performance in importance sampling tasks.

Simulation results demonstrate its potential benefits.

Abstract

In this paper we examine quantile-stratified samples from a known univariate probability distribution, with stratification occurring over a partition of the quantile regions in the distribution. We examine some general properties of this sampling method and we contrast it with standard IID sampling to highlight its similarities and differences. We examine the applications of this sampling method to various statistical simulations including importance sampling. We conduct simulation analysis to compare the performance of standard importance sampling against the quantile-stratified importance sampling to see how they each perform on a range of functions.