Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the quality of such estimators is to consider the variance over the total number of observations. In this paper we present a procedure to compute the variance of the estimator proposed by Kong and Valiant [Ann. Statist. 45 (5), pp. 2218 - 2247] for the case of Gaussian random vectors and provide a sharper bound than previously available.

翻译：蒙特卡洛矩阵迹估计是一种流行的随机化技术，通过对随机向量的多次观测结果中的二次型进行平均，来估计隐式定义矩阵的迹。分析此类估计量质量的最常用方法是考虑其方差与总观测次数的关系。本文提出了一种计算Kong和Valiant [Ann. Statist. 45 (5), pp. 2218 - 2247]所提估计量方差的计算方法，针对高斯随机向量的情况，给出了比现有结果更精确的界。