Hybrids of equidistribution and Monte Carlo methods of integration can
achieve the superior accuracy of the former while allowing the simple
error estimation methods of the latter. This paper studies the varian
ce of one such hybrid, scrambled nets, by applying a multidimensional
multiresolution (wavelet) analysis to the integrand. The integrand is
assumed to be measurable and square integrable but not necessarily of
bounded variation. In simple Monte Carlo, every nonconstant term of th
e multiresolution contributes to the variance of the estimated integra
l. For scrambled nets, certain low-dimensional and coarse terms do not
contribute to the variance. For any integrand in L-2, the sampling va
riance tends to zero faster under scrambled net quadrature than under
Monte Carlo sampling, as the number of function evaluations n tends to
infinity. Some finite n results bound the variance under scrambled ne
t quadrature by a small constant multiple of the Monte Carlo variance,
uniformly over all integrands f. Latin hypercube sampling is a specia
l case of scrambled net quadrature.