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Estimation of the Covariance Matrix

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Shrinkage Estimation for Mean and Covariance Matrices

Part of the book series: SpringerBriefs in Statistics ((JSSRES))

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Abstract

This chapter addresses decision-theoretic estimation of an error covariance matrix in a multivariate linear model relative to a Stein-type entropy loss. With a unified treatment for high and low dimensions, some important improving methods of the best scale and the best triangular invariant estimators are discussed by using the residual sum of squares matrix only. Also this chapter provides interesting dominance results by using the information on both the residual sum of squares matrix and the least squares estimator of the regression coefficient matrix.

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Authors and Affiliations

  1. Faculty of Medicine, Toho University, Tokyo, Japan

    Hisayuki Tsukuma

  2. Faculty of Economics, University of Tokyo, Tokyo, Japan

    Tatsuya Kubokawa

Authors
  1. Hisayuki Tsukuma
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  2. Tatsuya Kubokawa
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Correspondence to Hisayuki Tsukuma .

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Tsukuma, H., Kubokawa, T. (2020). Estimation of the Covariance Matrix. In: Shrinkage Estimation for Mean and Covariance Matrices. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-15-1596-5_7

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