On the asymptotic distribution of scrambled net quadrature

Recently, in a series of articles, Owen proposed the use of scrambled (t.m.s) nets and (t.s) sequences in high-dimensional numerical integration. These scrambled nets and sequences achieve the superior accuracy of equidistribution methods while allowing for the simpler error estimation techniques of Monte Carlo methods. The main aim of this article is to use Steinʹs method to study the asymptotic distribution of the scrambled (0.m.s) net integral estimate. In particular, it is shown that, for suitably smooth integrands on the s-dimensional unit hypercube, the estimate has an asymptotic normal distribution.