A class of R\'{e}nyi information estimators for multidimensional densities

Understand

A class of estimators of the R\'{e}nyi and Tsallis entropies of an unknown distribution $f$ in $\mathbb{R}^m$ is presented.

• These estimators are based on the $k$th nearest-neighbor distances computed from a sample of $N$ i.i.d.
• vectors with distribution $f$.
• We show that entropies of any order $q$, including Shannon's entropy, can be estimated consistently with minimal assumptions on $f$.