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Reproducing Ledoit–Wolf Covariance Shrinkage Results

Article Quant Q&A · Author: Matteo Campagnoli
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Summary

The document raises a replication question about Ledoit and Wolf’s covariance matrix shrinkage method. The author is trying to reproduce a plot relating Percentage Relative Improvement in Average Loss (PRIAL) to the ratio of the number of variables to the sample size, and reports difficulty obtaining similar results with an existing implementation.

The central issue is how the paper’s Monte Carlo samples were generated and whether those choices explain the mismatch. The post gives no sampling procedure, code details, reproduced values, or answer, so it does not establish which implementation or experimental setting is correct. It is useful as a pointer to a practical challenge in validating covariance estimators: PRIAL results may depend on the simulation design, and reproducing a published curve requires matching that design.

Key ideas

  • The post concerns replication of a covariance shrinkage paper’s simulation results.
  • PRIAL is examined as a function of the dimension-to-sample-size ratio.
  • The author suspects Monte Carlo sampling choices may explain the mismatch.
  • No solution or specific simulation settings are provided.

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StatisticsPortfolio constructionBacktesting
Full text
# Ledoit - Wolf Shrinkage: reproducing the paper results


# Ledoit - Wolf Shrinkage: reproducing the paper results












I've been trying to replicate the results of the paper A Well-Conditioned Estimator For Large-Dimensional Covariance Matrices by Ledoit and Wolf (2004). In particular, I'm having difficulties with the following plot

The graph is meant to study the relation between the Percentage Relative Improvement in Average Loss (PRIAL) with respect to the ratio $p/n$. I've been using the implementation provided here here, which I believe is correct. What I don't understand is the sampling process of the Monte Carlo simulation. I can't seem to obtain similar results

Has anyone ever tried to reproduce the paper? Do you have encoutered similar problems when studying the dynamics of the PRIAL?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.