Estimating Functionals Related to a Density by a Class of Statistics Based on Spacings
研究利用样本间距构造的一类统计量来估计概率密度的泛函，证明其几乎必然一致收敛，并重点推导了熵估计的渐近正态性及有效性条件。
We consider estimation of functionals of a probability density of the elements of a sample. We discuss a class of statistics based on spacings of increasing order and show that these statistics are almost surely consistent. Special attention is paid to entropy estimation. In particular we derive asymptotic normality in that case. It turns out that the entropy estimator is efficient under certain conditions on the unknown density.