This paper deals with certain estimation problems involving the covariance matrix in large dimensions. Due to the breakdown of finite-dimensional asymptotic theory when the dimension is not negligible with respect to the sample size, it is necessary to resort to an alternative framework known as...

It is well known that non-normality plays an important role in asset and risk management. However, handling a large number of assets has long been a challenge due to the curse of dimensionality. We describe a statistical technique, which we call Moment Component Analysis (MCA), that extends...

We consider sample covariance matrices constructed from real or complex i.i.d. variates with finite 12th moment. We assume that the population covariance matrix is positive definite and its spectral measure almost surely converges to some limiting probability distribution as the number of...