Random uniform approximation under weighted importance sampling of a class of stratified input

TL;DR

This paper analyzes the expected discrepancy in stratified input sampling using weighted importance sampling, providing bounds that improve error estimates for integral approximation.

Contribution

It introduces an upper bound for the expected Lp-discrepancy under weighted stratified sampling, enhancing understanding of integral approximation errors.

Findings

Derived an upper bound for expected Lp-discrepancy

Improved error estimates for weighted importance sampling

Applicable to stratified input sampling methods

Abstract

We consider random discrepancy under weighted importance sampling of a class of stratified input. We give the expected $L_p-$discrepancy($2\leq p<\infty$) upper bound in weighted form under a class of stratified sampling. This result contributes to the error estimate of the upper bound of the integral approximation under weighted importance sampling, and and our sampling pattern is a stratified input.