TY - GEN

T1 - Some large deviations results for Latin Hypercube sampling

AU - Drew, Shane S.

AU - Homem-de-Mello, Tito

PY - 2005

Y1 - 2005

N2 - Large deviations theory is a well-studied area which has shown to have numerous applications. The typical results, however, assume that the underlying random variables are either i.i.d. or exhibit some form of Markovian dependence. Our interest in this paper is to study the validity of large deviations results in the context of estimators built with Latin Hypercube sampling, a well-known sampling technique for variance reduction. We show that a large deviation principle holds for Latin Hypercube sampling for functions in one dimension and for separable multi-dimensional functions. Moreover, the upper bound of the probability of a large deviation in these cases is no higher under Latin Hypercube sampling than it is under Monte Carlo sampling. We extend the latter property to functions that preserve negative dependence (such as functions that are monotone in each argument). Numerical experiments illustrate the theoretical results presented in the paper.

AB - Large deviations theory is a well-studied area which has shown to have numerous applications. The typical results, however, assume that the underlying random variables are either i.i.d. or exhibit some form of Markovian dependence. Our interest in this paper is to study the validity of large deviations results in the context of estimators built with Latin Hypercube sampling, a well-known sampling technique for variance reduction. We show that a large deviation principle holds for Latin Hypercube sampling for functions in one dimension and for separable multi-dimensional functions. Moreover, the upper bound of the probability of a large deviation in these cases is no higher under Latin Hypercube sampling than it is under Monte Carlo sampling. We extend the latter property to functions that preserve negative dependence (such as functions that are monotone in each argument). Numerical experiments illustrate the theoretical results presented in the paper.

UR - http://www.scopus.com/inward/record.url?scp=33846693183&partnerID=8YFLogxK

U2 - 10.1109/WSC.2005.1574308

DO - 10.1109/WSC.2005.1574308

M3 - Conference contribution

AN - SCOPUS:33846693183

SN - 0780395204

SN - 9780780395206

T3 - Proceedings - Winter Simulation Conference

SP - 673

EP - 681

BT - Proceedings of the 2005 Winter Simulation Conference

Y2 - 4 December 2005 through 7 December 2005

ER -