Robust estimation with latin hypercube sampling: a central limit theorem for Z-estimators

TL;DR

This paper extends convergence results for Latin hypercube sampling to Z-estimators, deriving their asymptotic variance and establishing a CLT, thus providing a theoretical basis for LHS's improved efficiency in statistical estimation.

Contribution

It introduces a CLT for Z-estimators under LHS and quantifies the variance reduction compared to i.i.d. sampling.

Findings

LHS reduces the asymptotic variance of Z-estimators.

A Central Limit Theorem is established for Z-estimators with LHS.

LHS improves the efficiency of statistical estimators.

Abstract

Latin hypercube sampling (LHS) is a widely used stratified sampling method in computer experiments. In this work, we extend the existing convergence results for the sample mean under LHS to the broader class of $Z$-estimators, estimators defined as the zeros of a sample mean function. We derive the asymptotic variance of these estimators and demonstrate that it is smaller when using LHS compared to traditional independent and identically distributed (i.i.d.) sampling. Furthermore, we establish a Central Limit Theorem for $Z$-estimators under LHS, providing a theoretical foundation for its improved efficiency.