论文标题
有效的重要性抽样对正高斯二次形式的左尾
Efficient Importance Sampling for the Left Tail of Positive Gaussian Quadratic Forms
论文作者
论文摘要
在高斯随机矢量中估算二次形式的左尾在许多应用中至关重要。在这封信中，我们提出了一个有效的重要性采样估计器，该估计量具有限制的相对误差属性。与幼稚的蒙特卡洛（MC）相比，该属性大大减少了所提出的估计器所需的模拟运行次数，尤其是当感兴趣的概率很小时。提供了所选的仿真结果，以说明与天真MC以及一些众所周知的近似值相比，我们的估计量的效率。
Estimating the left tail of quadratic forms in Gaussian random vectors is of major practical importance in many applications. In this letter, we propose an efficient importance sampling estimator that is endowed with the bounded relative error property. This property significantly reduces the number of simulation runs required by the proposed estimator compared to naive Monte Carlo (MC), especially when the probability of interest is very small. Selected simulation results are presented to illustrate the efficiency of our estimator compared to naive MC as well as some of the well-known approximations.
