Improved second order estimation in the singular multivariate normal model

Didier Chételat, Martin T. Wells

Abstract: We consider the problem of estimating covariance and precision matrices, and their associated discriminant coefficients, from normal data when the rank of the covariance matrix is strictly smaller than its dimension and the available sample size. Using unbiased risk estimation, we construct novel estimators by minimizing upper bounds on the difference in risk over several classes. Our proposal estimates are empirically demonstrated to offer substantial improvement over classical approaches. Previous article in issue Next article in issue AMS 2000 subject classifications primary 62C15 secondary 62F10 62H12