Hilbert space analysis of latin hypercube sampling (Q2701646)

The main aim of the paper is the error asymptotics of latin hypercube sampling. The author proposes an explicit approach to the latin hypercube sampling based on the orthogonal projections in an appropriate Hilbert space related to the ANOVA decomposition in order to allow for a rigorous error analysis. Moreover, it is shown that the convergence cannot be uniformly superior to independent sampling on the class of square integrable functions. General conditions are established under which uniformity can be achieved, thereby indicating the role of certain Sobolev spaces. The material is presented in such a way that also surveys previous results. Hilbert space technique is used throughout.