Open Access
2019 Discrete minimax estimation with trees
Luc Devroye, Tommy Reddad
Electron. J. Statist. 13(2): 2595-2623 (2019). DOI: 10.1214/19-EJS1586

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.

Citation

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Luc Devroye. Tommy Reddad. "Discrete minimax estimation with trees." Electron. J. Statist. 13 (2) 2595 - 2623, 2019. https://doi.org/10.1214/19-EJS1586

Information

Received: 1 December 2018; Published: 2019
First available in Project Euclid: 14 August 2019

zbMATH: 07104725
MathSciNet: MR3992499
Digital Object Identifier: 10.1214/19-EJS1586

Subjects:
Primary: 60G07

Keywords: convex density , Density estimation , discrete probability distribution , Histogram , minimax theory , monotone density , Vapnik-Chervonenkis dimension

Vol.13 • No. 2 • 2019
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