Improved estimation of a covariance matrix in an elliptically contoured matrix distribution

Pui Lam Leung and Foon Yip Ng

Journal of Multivariate Analysis, 2004, vol. 88, issue 1, 131-137

Abstract: In this paper, the problem of estimating the covariance matrix of the elliptically contoured distribution (ECD) is considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean is proposed. It is shown that this new estimator dominates the unbiased estimator under the squared error loss function. Two special classes of ECD, namely, the multivariate-elliptical t distribution and the [var epsilon]-contaminated normal distribution are considered. A simulation study is carried out and indicates that this new shrinkage estimator provides a substantial improvement in risk under most situations.

Keywords: Scale; matrix; Multivariate-elliptical; t; distribution; [var; epsilon]-Contaminated; distribution; Decision-theoretic; estimation; Kurtosis (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (3)

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