Asymptotic theory for multiple samples with random membership

TL;DR

This paper develops an asymptotic theoretical framework for statistics involving multiple samples with random group membership, addressing a gap in existing research.

Contribution

It introduces a flexible framework capable of handling both deterministic and random memberships, with proven asymptotic properties and applications to stratified sampling.

Findings

Established asymptotic properties for the proposed framework

Demonstrated applicability to stratified sampling scenarios

Extended existing asymptotic theory to random membership contexts

Abstract

A statistic can be a function of multiple samples. There is little existing work on asymptotic theory for such statistics when group membership is random. We propose a flexible framework that can handle both deterministic and random membership. We prove some asymptotic properties and apply the framework to the stratified sampling context.