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.

翻译：我们研究估计E(g(X))的问题，其中g是d元实值函数，X是具有给定协方差矩阵的d维高斯向量。我们提出了一种新的E(g(X))无偏估计量，该估计量将随机降维技术与主成分分析相结合。在适当条件下，我们证明该算法的性能优于标准蒙特卡洛方法，效率提升达d阶量级。