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Editorial: Special Issue on "Nonparametric Inference Under Shape Constraints"

Published version
Peer-reviewed

Type

Article

Change log

Authors

Samworth, Richard J 
Sen, Bodhisattva 

Abstract

Shape-constrained inference usually refers to nonparametric function estimation and uncertainty quantification under qualitative shape restrictions such as monotonicity, convexity, log-concavity and so on. One of the earliest contributions to the field was by Grenander (1956). Motivated by the theory of mortality measurement, he studied the nonparametric maximum likelihood estimator of a decreasing density function on the nonnegative half-line. A great attraction of this estimator is that, unlike other nonparametric density estimators such as histograms or kernel density estimators, there are no tuning parameters (e.g., bandwidths) to choose.

Description

Keywords

49 Mathematical Sciences, 4905 Statistics

Journal Title

STATISTICAL SCIENCE

Conference Name

Journal ISSN

0883-4237
2168-8745

Volume Title

33

Publisher

Institute of Mathematical Statistics

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/N031938/1)
Engineering and Physical Sciences Research Council (EP/P031447/1)
R. J. Samworth is supported by EPSRC Grants EP/P031447/1 and EP/N031938/1. B. Sen is supported by NSF Grants DMS-17-12822 and AST-16-14743.