# Discrete minimax estimation with trees

## TL;DR

This paper introduces a recursive partitioning method for density estimation that achieves optimal $L_1$ minimax rates for certain discrete nonparametric classes, enhancing nonparametric density estimation techniques.

## Contribution

The paper presents a novel recursive partitioning scheme that effectively estimates densities and attains optimal minimax rates in discrete settings.

## Key findings

- Achieves optimal $L_1$ minimax rates for specific classes.
- Provides a simple, recursive data-based partitioning approach.
- Demonstrates effectiveness in discrete nonparametric density estimation.

## Abstract

We propose a simple recursive data-based partitioning scheme which produces piecewise-constant or piecewise-linear density estimates on intervals, and show how this scheme can determine the optimal $L_1$ minimax rate for some discrete nonparametric classes.