Berry-Esseen bounds are derived for the plug-in estimator of a class of diversity indices including Simpson's and Rényi's, plus explicit bounds for Shannon entropy using plug-in, Miller-Madow, and jackknife estimators on countable alphabets.
Shannon, A mathematical theory of communication
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Berry-Esseen bounds for estimators of entropy and diversity indices on countable alphabets
Berry-Esseen bounds are derived for the plug-in estimator of a class of diversity indices including Simpson's and Rényi's, plus explicit bounds for Shannon entropy using plug-in, Miller-Madow, and jackknife estimators on countable alphabets.