The Markowitz mean-variance framework is the foundation of modern portfolio theory. One problem with this approach, however, is how sample covariance matrices tend to underestimate risk. Since the biases of optimized portfolios are closely related to eigenfactor portfolios, we present a...

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem for linear spectral statistics of the sample covariance matrix based on self-normalized observations. For testing sphericity, our tests neither assume...

This paper establishes asymptotic properties for spiked empirical eigenvalues of sample co- variance matrices for high-dimensional data with both cross-sectional dependence and a dependent sample structure. A new finding from the established theoretical results is that spiked empirical...

Limit spectral theory of sample covariance matrices of increasing dimension was recently used as a base for the development of improved non-degenerating methods of multivariate statistical analysis. We present results of a numerical investigation of fundamental relations of this theory (of the...