Computable Bernstein Certificates for Cross-Fitted Clipped Covariance Estimation
This work addresses robust covariance estimation for statistical analysis in the presence of outliers, representing an incremental improvement with a principled tuning method.
The paper tackles robust covariance estimation from heavy-tailed data with outliers by proposing a cross-fitted clipped estimator with computable Bernstein certificates, enabling data-driven tuning via a selector that balances error and bias, achieving stable performance and competitive accuracy in experiments.
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.