@article {IOPORT.06102109,
    author       = {Drew, Shane S. and Homem-de-Mello, Tito},
    title        = {Some large deviations results for Latin hypercube sampling.},
    year         = {2012},
    journal      = {Methodology and Computing in Applied Probability},
    volume       = {14},
    number       = {2},
    issn         = {1387-5841},
    pages        = {203-232},
    publisher    = {Springer, Norwell, MA},
    doi          = {10.1007/s11009-010-9200-0},
    abstract     = {The authors of this paper, motivated by applications in stochastic optimization, study large deviations theory. In particular, the paper deals with sample average approximations of probabilities of certain types of rare events. A common approach to sample average approximations is to use Monte Carlo sampling, i.e., i.i.d. random samples. As there are some well-known drawbacks of Monte Carlo methods, the authors study an alternative approach here, namely a sampling technique for variance reduction known as Latin Hypercube sampling. The authors show that large deviations results can also hold for a Latin Hypercube approach. It is shown in this paper that a large deviations principle holds for this method for functions in one variable, and for separable functions in multiple variables with no or a bounded residual term in the ANOVA decomposition, and for functions in multiple variables which are monotone in each argument. It is also shown that the bound for the probability of a large deviation in these cases using Latin Hypercube sampling does not exceed the bound using Monte Carlo sampling. A section on numerical results concludes the paper.},
    reviewer     = {Peter Kritzer (Linz)},
    identifier   = {06102109},
}