On generalized expectation-based estimation of a population spectral distribution from high-dimensional data

This paper discusses the problem of estimating the population spectral distribution from high-dimensional data. We present a general estimation procedure that covers situations where the moments of this distribution fail to identify the model parameters. The main idea is to use generalized functional expectations as a substitute for the moments. Beyond the consistency, we also prove a central limit theorem for the proposed estimator. Simulation experiments illustrate the implementation of the estimation procedure. An application to the analysis of the eigenvalues of the sample correlation matrix of S&P 500 daily stock returns is proposed. Copyright The Institute of Statistical Mathematics, Tokyo 2015