固定k近邻密度泛函估计的双样本分析
Finite-Sample Analysis of Fixed-k Nearest Neighbor Density Functional Estimators
摘要：
我们提供有限样本分析的一般框架，使用k-最近邻统计估计泛函的非参数连续概率密度，包括熵和发散。不是将一致的密度估计值（这需要$k \to \infty$作为样本量$n \to \infty$）插入到感兴趣的泛函中，而是考虑固定k并执行偏差校正的估计值。这在计算上更有效，并且正如我们在某些情况下所示，在统计上，导致更快的收敛速度。我们的框架统一了几个以前的估计，其中大部分是我们的第一个有限样本保证。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
