Efficient Nonparametric Estimation of Mixture Proportions
通过构造多项分布近似和最大似然估计序列，推导了混合比例非参数估计的Cramér-Rao下界，并刻画了渐近最优估计量。
SUMMARY By constructing a sequence of multinomial approximations and related maximum likelihood estimators, we derive a Cramér-Rao lower bound for nonparametric estimators of the mixture proportions and thereby characterize asymptotically optimal estimators. For the case of the sampling model M2 of Hosmer (1973) it is shown that the sequence of maximum likelihood estimators, which can be obtained explicitly, is asymptotically optimal in this sense. The results hold true even when the multinomial approximations involve cells chosen adaptively, from the data, in a well-specified way.