  We present a new unbiased algorithm that estimates the expected value of f(U)
via Monte Carlo simulation, where U is a vector of d independent random
variables, and f is a function of d variables. We assume that f does not depend
equally on all its arguments. Under certain conditions we prove that, for the
same computational cost, the variance of our estimator is lower than the
variance of the standard Monte Carlo estimator by a factor of order d. Our
method can be used to obtain a low-variance unbiased estimator for the
expectation of a function of the state of a Markov chain at a given time-step.
We study applications to volatility forecasting and time-varying queues.
Numerical experiments show that our algorithm dramatically improves upon the
standard Monte Carlo method for large values of d, and is highly resilient to
discontinuities.
