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Copy file name to clipboardExpand all lines: LITERATURE.md
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@@ -7,6 +7,22 @@ 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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## Weighted Average Ensemble for Cholesky-based Covariance Matrix Estimation [arxiv](https://arxiv.org/pdf/2503.15991)
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Xiaoning Kang, Zhenguo Gao, Xi Liang and Xinwei Deng
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The modified Cholesky decomposition (MCD) is an efficient technique for estimating
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a covariance matrix. However, it is known that the MCD technique often requires
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a pre-specified variable ordering in the estimation procedure. In this work, we propose a weighted average ensemble covariance estimation for high-dimensional data
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based on the MCD technique. It can flexibly accommodate the high-dimensional
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case and ensure the positive definiteness property of the resultant estimate. Our key
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idea is to obtain different weights for different candidate estimates by minimizing
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an appropriate risk function with respect to the Frobenius norm. Different from
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the existing ensemble estimation based on the MCD, the proposed method provides
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a sparse weighting scheme such that one can distinguish which variable orderings
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employed in the MCD are useful for the ensemble matrix estimate. The asymptotically theoretical convergence rate of the proposed ensemble estimate is established
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under regularity conditions. The merits of the proposed method are examined by
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the simulation studies and a portfolio allocation example of real stock data.
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