Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation

• URL: http://arxiv.org/abs/2602.14020v1
• Date: Sun, 15 Feb 2026 06:53:40 GMT
• Title: Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation
• Authors: Even He, Zaizai Yan,
• Abstract summary: We propose a cross-fitted clipped covariance estimator equipped with emphfully computable Bernstein-type deviation certificates.<n>The resulting procedure adapts to intrinsic complexity measures such as effective rank under mild tail regularity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study operator-norm covariance estimation from heavy-tailed samples that may include a small fraction of arbitrary outliers. A simple and widely used safeguard is \emph{Euclidean norm clipping}, but its accuracy depends critically on an unknown clipping level. We propose a cross-fitted clipped covariance estimator equipped with \emph{fully computable} Bernstein-type deviation certificates, enabling principled data-driven tuning via a selector (\emph{MinUpper}) that balances certified stochastic error and a robust hold-out proxy for clipping bias. The resulting procedure adapts to intrinsic complexity measures such as effective rank under mild tail regularity and retains meaningful guarantees under only finite fourth moments. Experiments on contaminated spiked-covariance benchmarks illustrate stable performance and competitive accuracy across regimes.

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