Adaptive optimal allocation in stratified sampling methods

TL;DR

This paper introduces an adaptive stratified sampling algorithm that dynamically adjusts sampling proportions to minimize variance, achieving asymptotic optimality and confirmed efficiency through numerical experiments.

Contribution

It presents a novel adaptive allocation method in stratified sampling that converges to the optimal variance-minimizing proportions.

Findings

Proposed algorithm converges to optimal allocation.

Stratified estimator is asymptotically normal.

Numerical experiments demonstrate efficiency.

Abstract

In this paper, we propose a stratified sampling algorithm in which the random drawings made in the strata to compute the expectation of interest are also used to adaptively modify the proportion of further drawings in each stratum. These proportions converge to the optimal allocation in terms of variance reduction. And our stratified estimator is asymptotically normal with asymptotic variance equal to the minimal one. Numerical experiments confirm the efficiency of our algorithm.