Title: Eigen-inference by Marchenko-Pastur inversion Show Chinese title

Title: 通过Marchenko-Pastur反演的特征推断

Abstract: A new method of estimating population linear spectral statistics from high-dimensional data is introduced. When the dimension $d$ grows with the sample size $n$ such that $\frac{d}{n} \rightarrow c>0$, the introduced method is the first to provably achieve eigen-inference with fast convergence rates of $\mathcal{O}(n^{\varepsilon-1})$ for any $\varepsilon > 0$ in the general non-parametric setting. This is achieved though a novel Marchenko-Pastur inversion formula, which may also be formulated as a semi-explicit solution to the Marchenko-Pastur equation. Show Chinese abstract

Abstract: 一种从高维数据中估计总体线性谱统计量的新方法被引入。 当维度$d$随样本量$n$增长，使得$\frac{d}{n} \rightarrow c>0$时，所引入的方法是第一个在一般非参数设置下对任何$\varepsilon > 0$能够证明以快速收敛率$\mathcal{O}(n^{\varepsilon-1})$实现特征值推断的方法。 这是通过一个新颖的Marchenko-Pastur逆公式实现的，该公式也可以表述为Marchenko-Pastur方程的半显式解。