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November 2018 Limit Theory in Monotone Function Estimation
Cécile Durot, Hendrik P. Lopuhaä
Statist. Sci. 33(4): 547-567 (November 2018). DOI: 10.1214/18-STS664

Abstract

We give an overview of the different concepts and methods that are commonly used when studying the asymptotic properties of isotonic estimators. After introducing the inverse process, we illustrate its use in establishing weak convergence of the estimators at a fixed point and also weak convergence of global distances, such as the $\mathbb{L}_{p}$-distance and supremum distance. Furthermore, we discuss the developments on smooth isotonic estimation.

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Cécile Durot. Hendrik P. Lopuhaä. "Limit Theory in Monotone Function Estimation." Statist. Sci. 33 (4) 547 - 567, November 2018. https://doi.org/10.1214/18-STS664

Information

Published: November 2018
First available in Project Euclid: 29 November 2018

zbMATH: 07032829
MathSciNet: MR3881208
Digital Object Identifier: 10.1214/18-STS664

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.33 • No. 4 • November 2018
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