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arXiv · 2607.19825

Mens: Nonlinear shrinkage estimation in nonparanormal models for financial applications

Hamid Karamikabir·Mohammad Arashi
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Abstract

We develop a theory of nonlinear shrinkage covariance estimation for nonparanormal (Gaussian-copula) models, in which each observed coordinate is an unknown strictly increasing transformation of a latent Gaussian vector. This model accommodates arbitrary marginal skewness and heavy marginal tails while retaining a Gaussian dependence structure, and it is the natural semiparametric setting for heavy-tailed, asymmetric financial returns. Our estimator, marginal-free nonlinear shrinkage (MENS), applies an oracle nonlinear shrinkage function to the eigenvalues of the normal-scores rank-covariance matrix. We give the almost-sure convergence of the empirical spectral distribution of the normal-scores covariance to the generalized Marchenko-Pastur law of Sigma, and asymptotic optimality of MENS among rotation-equivariant estimators under Frobenius loss. We establish a Baik-Ben Arous-Peche phase transition for spiked latent correlations. The MENS attains the robustness of rank-based estimation and the efficiency of nonlinear shrinkage at once within this class. We corroborate the theory with a simulation study that isolates the marginal-invariance property and the spiked transition. In an out-of-sample minimum-variance backtest on S&P 500 stocks, MENS delivers a better-conditioned covariance estimate, lower realized portfolio volatility, and lower turnover than linear shrinkage, illustrating its practical value for high-dimensional allocation and decision-making.

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BibTeXRIS

Hamid Karamikabir, Mohammad Arashi. 2026-07-22. Mens: Nonlinear shrinkage estimation in nonparanormal models for financial applications. https://arxiv.org/abs/2607.19825

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