LOCAL MOMENT ESTIMATION OF POPULATION SPECTRUM 1 A LOCAL MOMENT ESTIMATOR OF THE SPECTRUM OF A LARGE DIMENSIONAL COVARIANCE MATRIX

Abstract: This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment estimation procedure. Compared with the original one, the new proce-dure can be applied successfully to models where the asymptotic clusters of sample eigenvalues generated by different population eigenvalues are not all separate. The proposed estimates are proved to be consistent. Numerical results illustrate the im-plementation of the estimation procedure and demonstrate its efficiency in various cases. Key words and phrases: Empirical spectral distribution, Large covariance matrix