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

arXiv: https://arxiv.org/abs/1606.01554 · HTML: https://mlsanity.com/paper/1606.01554/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2016.

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## Abstract (arXiv)

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 → ∞ as the sample size n → ∞) 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.