Rare-event analysis for extremal eigenvalues of white Wishart matrices
研究了高维白Wishart矩阵极端特征值的尾部概率，给出了渐近近似和边界，并设计了高效的蒙特卡洛模拟算法，在性能上优于现有方法。
In this paper, we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature $p$ is much larger than or comparable to the number of observations $n$, a common situation in modern data analysis. We provide asymptotic approximations and bounds for the tail probabilities of the extremal eigenvalues. Moreover, we construct efficient Monte Carlo simulation algorithms to compute the tail probabilities. Simulation results show that our method has the best performance among known approximation approaches, and furthermore provides an efficient and accurate way for evaluating the tail probabilities in practice.