November 14, 2025StatOpen Access

Matrix Freedman Inequality for Sub‐Weibull Martingales

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Analysis reveals improved covariance estimation thresholds in sub-Weibull martingales, suggesting greater confidence in high-stakes scenarios.

New matrix Freedman inequality improves thresholds for covariance estimation in sub-Weibull martingales, enhancing confidence levels in applications.
Key findings demonstrate that the top eigenvalue's tail bound maintains non-asymptotic properties, directly benefiting covariance estimation.
Analysis of simulations indicates effective applications for self-normalized confidence sets in stochastic linear bandits, showcasing high confidence thresholds.
The findings highlight significant implications for understanding martingale behavior under sub-Weibull conditions, warranting further exploration in related domains.

Íñigo Torres (2025) studied this question.

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Analysis reveals improved covariance estimation thresholds in sub-Weibull martingales, suggesting greater confidence in high-stakes scenarios.