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We consider the problem of estimating covariance and precision matrices, andtheir associated discriminant coefficients, from normal data when the rank ofthe covariance matrix is strictly smaller than its dimension and the availablesample size. Using unbiased risk estimation, we construct novel estimators byminimizing upper bounds on the difference in risk over several classes. Ourproposal estimates are empirically demonstrated to offer substantialimprovement over classical approaches.

Improved Second Order Estimation in the Singular Multivariate Normal Model