Linear Shrinkage of Sample Covariance Matrix or Matrices Under Elliptical Distributions: A Review

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A3 Kirjan tai muun kokoomateoksen osa

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en

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31

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This chapter reviews methods for linear shrinkage of the sample covariance matrix (SCM) and matrices (SCM-s) under elliptical distributions in single and multiple populations settings, respectively. In the single sample setting a popular linear shrinkage estimator is defined as a linear combination of the sample covariance matrix (SCM) with a scaled identity matrix. The optimal shrinkage coefficients minimizing the mean-squared error (MSE) under elliptical sampling are shown to be functions of few key parameters only, such as elliptical kurtosis and sphericity parameter. Similar results and estimators are derived for multiple population settings and applications of the studied shrinkage estimators are illustrated in portfolio optimization.

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Publisher Copyright: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

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Ollila, E 2024, Linear Shrinkage of Sample Covariance Matrix or Matrices Under Elliptical Distributions : A Review. in Elliptically Symmetric Distributions in Signal Processing and Machine Learning. Springer, pp. 79-109. https://doi.org/10.1007/978-3-031-52116-4_3