Density Estimation with Contaminated Data: Minimax Rates and Theory of Adaptation

Understand

This paper studies density estimation under pointwise loss in the setting of contamination model.

• The goal is to estimate $f(x_0)$ at some $x_0\in\mathbb{R}$ with i.i.d.
• observations, $$ X_1,\dots,X_n\sim (1-\epsilon)f+\epsilon g, $$ where $g$ stands for a contamination distribution.
• In the context of multiple testing, this can be interpreted as estimating the null density at a point.