Improved second order estimation in the singular multivariate normal model

Didier Chételat and Martin T. Wells

Journal of Multivariate Analysis, 2016, vol. 147, issue C, 1-19

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.

Keywords: Covariance matrix; Precision matrix; Discriminant function; LDA; Unbiased risk estimator; Moore–Penrose inverse; Singular normal; Singular Wishart (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.jmva.2016.01.001

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