A well-conditioned estimator for large-dimensional covariance matrices
Journal of Multivariate Analysis
Simultaneous modelling of the Cholesky decomposition of several covariance matrices
Journal of Multivariate Analysis
Shrinkage estimation of high dimensional covariance matrices
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
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Many applications require an estimate for the covariance matrix that is non-singular and well-conditioned. As the dimensionality increases, the sample covariance matrix becomes ill-conditioned or even singular. A common approach to estimating the covariance matrix when the dimensionality is large is that of Stein-type shrinkage estimation. A convex combination of the sample covariance matrix and a well-conditioned target matrix is used to estimate the covariance matrix. Recent work in the literature has shown that an optimal combination exists under mean-squared loss, however it must be estimated from the data. In this paper, we introduce a new set of estimators for the optimal convex combination for three commonly used target matrices. A simulation study shows an improvement over those in the literature in cases of extreme high-dimensionality of the data. A data analysis shows the estimators are effective in a discriminant and classification analysis.