Limit Theory in Monotone Function Estimation

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Limit Theory in Monotone Function Estimation

Journal Article (2018)

Author(s)

Cécile Durot (Paris Nanterre University)

Hendrik P. Lopuhaä (TU Delft - Statistics)

Cox model Maximum likelihood estimators Isotonic estimation Monotone density Current status model Limit theory Lp-distance Monotone failure rate Monotone regression Supremum distance

DOI related publication

https://doi.org/10.1214/18-STS664 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:95f1cb4b-bb91-4671-8796-2d54b9fd7c94

More Info

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Publication Year

2018

Language

English

Issue number

4

Volume number

33

Pages (from-to)

547-567

Downloads counter

153

Abstract

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 Lp-distance and supremum distance.
Furthermore, we discuss the developments on smooth isotonic estimation.