Simulating Gaussian vectors via randomized dimension reduction and PCA

We study the problem of estimating E(g(X)), where g is a real-valued function of d variables and X is a d-dimensional Gaussian vector with a given covariance matrix. We present a new unbiased estimator for E(g(X)) that combines the randomized dimension reduction technique with principal components analysis. Under suitable conditions, we prove that our algorithm outperforms the standard Monte Carlo method by a factor of order d.