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arXiv · 2504.03390

Estimation of Population Linear Spectral Statistics by Marchenko--Pastur Inversion

Ben Deitmar
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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 $\frac{d}{n} \to c>0$, the proposed method is the first with proven convergence rate of $\mathcal{O}(n^{\varepsilon - 1})$ for any $\varepsilon > 0$ in a general nonparametric setting. For Gaussian data, a CLT for the estimation error with normalization factor $n$ is shown.

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Ben Deitmar. 2025-04-04. Estimation of Population Linear Spectral Statistics by Marchenko--Pastur Inversion. https://arxiv.org/abs/2504.03390

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