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math.PR2026
Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets
Zhen Hong Yu, Yu Miao
In the present paper, we derive Berry-Esseen bounds for the estimation of diversity indices on countable alphabets. A general non-asymptotic convergence rate is established for the…
math.PR2024
Some asymptotic behaviors for the plug-in estimator of entropy
Zhenhong Yu, Yu Miao
In the present paper, we consider the plug-in estimator of Shannon's entropy defined on a finite alphabet which is assumed to dynamically vary as the sample size increases. The asy…
math.PR2024
Large deviation inequalities for the nonlinear unbalanced urn model
Jianan Shi, Zhenhong Yu, Yu Miao
In the present paper, we consider the two-color nonlinear unbalanced urn model, under a drawing rule reinforced by an -valued concave function and an unbalanced repla…