The asymptotic efficiency of Good's nonparametric coverage estimator is obtained relative to the best estimator derived under the assumption that all classes are equally likely. Even when that assumption is true, Good's estimator is quite efficient, with an asymptotic relative efficiency of greater than 85% in all cases, and greater than 95% if the expected coverage is less than one-half.
"The Efficiency of Good's Nonparametric Coverage Estimator." Ann. Statist. 14 (3) 1257 - 1260, September, 1986. https://doi.org/10.1214/aos/1176350066