Analysis of KNN Density Estimation

Understand

We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method.

• Our analysis includes two different cases depending on whether the support set is bounded or not.
• In the first case, the probability density function has a bounded support and is bounded away from zero.
• We show that kNN density estimation is minimax optimal under both $\ell_1$ and $\ell_\infty$ criteria, if the support set is known.