On the overestimation of the largest eigenvalue of a covariance matrix

2017/08/11 by Soufiane Hayou, Hayou, Soufiane
Computer Science · Mathematics · #FOS: Economics and business #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Finance (q-fin.MF) #Matrix Theory and Algorithms #Probability (math.PR) #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1708.03551

openalex publication_date 2017/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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