ON THE 2ND-ORDER STATISTICS OF THE EIGENVECTORS OF SAMPLE COVARIANCE MATRICES

Eigenvectors of sample covariance! matrices are used in a variety of s tatistical signal processing problems, The second-order statistics of these eigenvectors are needed to compute the variance of estimates bas ed on these eigenvectors Formulas for the second-order statistics of t he eigenvectors have been derived in the statistical literature and ar e widely used. In this correspondence, we point out a discrepancy betw een the statistics observed in numerical simulations and the theoretic al formulas, due to the nonuniqueness of the definition of eigenvector s, We present two ways to resolve this discrepancy. The first involves modifying the theoretical formulas to match the computational results . The second involved a simple modification of the computations to mak e them match existing formulas.