On the overestimation of the largest eigenvalue of a covariance matrix
classification
🧮 math.PR
math.STq-fin.MFstat.TH
keywords
eigenvaluelargestcovariancematrixproveapproachbiggerdimension
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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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