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@@ -7,6 +7,24 @@ In no particular order. The scope is robust diversified portfolios and things th
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Or file an [issue](https://github.com/microprediction/precise/issues).
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## Regularized Tyler’s Scatter Estimator: Existence, Uniqueness, and Algorithms [pdf](https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6879466)
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Ying Sun and Daniel P. Palomar
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This paper considers the regularized Tyler’s scatter
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estimator for elliptical distributions, which has received considerable attention recently. Various types of shrinkage Tyler’s estimators have been proposed in the literature and proved work effectively in the “large small ” scenario. Nevertheless, the existence
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and uniqueness properties of the estimators are not thoroughly
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studied, and in certain cases the algorithms may fail to converge.
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In this work, we provide a general result that analyzes the sufficient condition for the existence of a family of shrinkage Tyler’s
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estimators, which quantitatively shows that regularization indeed
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reduces the number of required samples for estimation and the
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convergence of the algorithms for the estimators. For two specific
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shrinkage Tyler’s estimators, we also proved that the condition is
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necessary and the estimator is unique. Finally, we show that the
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two estimators are actually equivalent. Numerical algorithms are
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also derived based on the majorization-minimization framework,
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under which the convergence is analyzed systematically.
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## James–Stein for the leading eigenvector [pdf](https://www.pnas.org/doi/epdf/10.1073/pnas.2207046120)
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Lisa Goldberg and Alec Kercheval
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