On the overestimation of the largest eigenvalue of a covariance matrix
Probability
2017-08-14 v1 Statistics Theory
Mathematical Finance
Statistics Theory
Abstract
In this paper, we use a new approach to prove that the largest eigenvalue of the sample covariance matrix of a normally distributed vector is bigger than the true largest eigenvalue with probability 1 when the dimension is infinite. We prove a similar result for the smallest eigenvalue.
Keywords
Cite
@article{arxiv.1708.03551,
title = {On the overestimation of the largest eigenvalue of a covariance matrix},
author = {Soufiane Hayou},
journal= {arXiv preprint arXiv:1708.03551},
year = {2017}
}
Comments
15 pages, 1 figure