Statistical Science

Limit Theory in Monotone Function Estimation

Cécile Durot and Hendrik P. Lopuhaä

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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.

Article information

Source
Statist. Sci., Volume 33, Number 4 (2018), 547-567.

Dates
First available in Project Euclid: 29 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.ss/1543482058

Digital Object Identifier
doi:10.1214/18-STS664

Mathematical Reviews number (MathSciNet)
MR3881208

Zentralblatt MATH identifier
07032829

Keywords
Cox model current status model isotonic estimation limit theory $\mathbb{L}_{p}$-distance maximum likelihood estimators monotone density monotone failure rate monotone regression supremum distance

Citation

Durot, Cécile; Lopuhaä, Hendrik P. Limit Theory in Monotone Function Estimation. Statist. Sci. 33 (2018), no. 4, 547--567. doi:10.1214/18-STS664. https://projecteuclid.org/euclid.ss/1543482058


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