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Asymptotic theory for multiple samples with random membership

Ha-Young Shin

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.

Asymptotic theory for multiple samples with random membership

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.
Paper Structure (5 sections, 4 theorems, 21 equations)

This paper contains 5 sections, 4 theorems, 21 equations.

Table of Contents

  1. Introduction
  2. Framework
  3. Application to stratified sampling
  4. Discussion
  5. Proofs

Key Result

Proposition 2.1

(a) For all $s\in\Xi$ and $j\in\mathbb{Z}^+$, $K_j^s$ is measurable, as are $Y_{(j)}^s$ and $S_{(j)}^s$. (b) For all $s\in\Xi$, $\{N_n^s,Y^s_{(1)},Y^s_{(2)},\ldots\}$ is independent and satisfies $Y_{(j)}^s\overset{d}=Y \mid (S=s)$ for all $j\in\mathbb{Z}^+$. (c) For all $m_1,\ldots,m_\xi\in\mathbb{

Theorems & Definitions (8)

  • Proposition 2.1
  • Proposition 2.2
  • Proposition 3.1
  • Proposition 3.2
  • proof : Proof of Proposition \ref{['iid']}
  • proof : Proof of Proposition \ref{['conv']}
  • proof : Proof of Proposition \ref{['cons']}
  • proof : Proof of Proposition \ref{['clt']}