Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Convergence rates of eigenvector empirical spectral distribution of large dimensional sample covariance matrix (1311.5000v2)

Published 20 Nov 2013 in math.ST and stat.TH

Abstract: The eigenvector Empirical Spectral Distribution (VESD) is adopted to investigate the limiting behavior of eigenvectors and eigenvalues of covariance matrices. In this paper, we shall show that the Kolmogorov distance between the expected VESD of sample covariance matrix and the Mar\v{c}enko-Pastur distribution function is of order $O(N{-1/2})$. Given that data dimension $n$ to sample size $N$ ratio is bounded between 0 and 1, this convergence rate is established under finite 10th moment condition of the underlying distribution. It is also shown that, for any fixed $\eta>0$, the convergence rates of VESD are $O(N{-1/4})$ in probability and $O(N{-1/4+\eta})$ almost surely, requiring finite 8th moment of the underlying distribution.

Summary

We haven't generated a summary for this paper yet.