2025/03/19 by Lamia Lamrani, Lamrani, Lamia, Christian Bongiorno +3 · 3 citations
Decision Sciences · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Portfolio Management (q-fin.PM) #Probability and Risk Models #Risk Management (q-fin.RM) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2503.15186
openalex publication_date 2025/03/19 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28
Cross-validation is a statistical tool that can be used to improve large covariance matrix estimation. Although its efficiency is observed in practical applications and a convergence result towards the error of the non linear shrinkage is available in the high-dimensional regime, formal proofs that take into account the finite sample size effects are currently lacking. To carry on analytical analysis, we focus on the holdout method, a single iteration of cross-validation, rather than the traditional k-fold approach. We derive a closed-form expression for the expected estimation error when the population matrix follows a white inverse Wishart distribution, and we observe the optimal train-test split scales as the square root of the matrix dimension. For general population matrices, we connected the error to the variance of eigenvalues distribution, but approximations are necessary. In this framework and in the high-dimensional asymptotic regime, both the holdout and k-fold cross-validation methods converge to the optimal estimator when the train-test ratio scales with the square root of the matrix dimension which is coherent with the existing theory.