Non-uniform Bound on Normal Approximation of Latin Hypercube Sampling

Kritsana Neammanee,Petcharat Rattanawong

doi:10.5539/jmr.v1n2p28

Abstract

Loh (Loh, W.L, 1996b) established a Berry-Esseen type bound for $W$, the random variable based on a latin hypercube sampling, to the standard normal distribution. He used an inductive approach of Stein's method to give the rate of convergence $\frac{C_d}{\sqrt{n}}$ without the value of $C_d.$ In this article, we use a concentration inequality approach of Stein's method to obtain a constant $C_d.$

Highlights

Introduction and Main ResultsLatin hypercube sampling(McKay, M.D., 1979) is a method of sampling that can be used to produce input values for estimation of integrals over multidimensional domains
The main feature of Latin hypercube sampling(LHS) is that, contrast to simple random sampling, it stratifies on all input dimensions simultaneously
For positive integers d and n, d ≥ 2, let: 1. πk, 1 ≤ k ≤ d, be random permutations of {1, ..., n} each uniformly distributed over all the n! possible permutations; 2

Summary

Introduction

Introduction and Main ResultsLatin hypercube sampling(McKay, M.D., 1979) is a method of sampling that can be used to produce input values for estimation of integrals over multidimensional domains. Πk, 1 ≤ k ≤ d, be random permutations of {1, ..., n} each uniformly distributed over all the n! Let X be a random vector uniformly distributed on [0, 1]d and f be a measurable function from [0, 1]d to R.

Results

Conclusion