אומדן מטריצת קובריאנס תחת פרטיות דיפרנציאלית

תקציר מקורי באנגליתarXiv:2603.19703v3 Announce Type: replace-cross Abstract: Estimating covariance matrices is fundamental to a wide range of statistical applications. This paper studies minimax and adaptive estimation of high-dimensional covariance matrices under $\rho$-zero-concentrated differential privacy ($\rho$-zCDP) over three nested classes: the pointwise-decay class $\mathcal{H}_\alpha$, the row-tail class $\mathcal{G}_\alpha$, and the separated-block class $\mathcal{F}_\alpha$. We consider both squared operator norm loss and normalized squared Frobenius norm loss. For $\mathcal{H}_\alpha$ and $\mathcal{G}_\alpha$, we develop center--outer dyadic estimators tailored to the refined geometry of the two classes, while for $\mathcal{F}_\alpha$, we develop a blockwise tridiagonal estimator. The resulting