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Good 非参数覆盖率估计量的效率
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.
随机样本覆盖概率非参数估计量的正态极限律
The coverage of a multinomial random sample is the sum of the probabilities of the observed classes. A normal limit law is rigorously proved for Good's (1953) coverage estimator. The result is valid under very general conditions and all terms except the coverage itself are observable. Nevertheless the implied confidence intervals are not much wider than those developed under restrictive assumptions such as in the classical occupancy problem. The asymptotic variance is…
低覆盖样本的覆盖量置信区间
The coverage of a random sample from a multinomial population is defined to be the sum of the probabilities of the observed classes. The problem is to estimate the coverage of a random sample given only the number of classes observed exactly once, twice, etc. This problem is related to the problem of estimating the number of classes in the population. Non-parametric confidence intervals are given when the coverage is low such that a Poisson approximation holds. These…