Paper Characterizes Tight Sample Bounds for Renyi and Min-Entropy Estimation

abeirami · x · 2026-08-19

The paper 'Tight Sample Bounds for Renyi and Min-Entropy Estimation' characterizes the sample complexity for estimating Rényi and min-entropy. It proves that estimating min-entropy to constant additive accuracy has a sample complexity of $\Theta(k\log k)$, requiring $\Theta(\log^2 k)$ more samples than Shannon entropy and correcting a prior $\Theta(k/\log k)$ characterization. For integer orders $\alpha$ ($2 \le \alpha \le c0 \log k$), it establishes matching bounds of $\Theta(\alpha k^{1-1/\alpha})$, showing the factor $\alpha$ is unavoidable.

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