标题： 固定-k最近邻密度泛函估计量的有限样本分析 显示英文标题

标题： Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators

摘要： 我们对一个使用k近邻统计量估计非参数连续概率密度泛函（包括熵和发散度）的通用框架进行了有限样本分析。 与将一致的概率密度估计值（样本量为$k \to \infty$时收敛到$n \to \infty$）代入目标泛函的方法不同，我们考虑的估计器固定k值并进行偏差校正。 这种方法在计算上更加高效，并且如我们在某些情况下所展示的，统计上也更有效，从而实现更快的收敛速度。 我们的框架统一了若干先前的估计器，对于其中大多数估计器，我们的工作首次提供了有限样本保证。 显示英文摘要

摘要： We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires $k \to \infty$ as the sample size $n \to \infty$) into the functional of interest, the estimators we consider fix k and perform a bias correction. This is more efficient computationally, and, as we show in certain cases, statistically, leading to faster convergence rates. Our framework unifies several previous estimators, for most of which ours are the first finite sample guarantees.