Editorial: Special Issue on "Nonparametric Inference Under Shape Constraints"
Published version
Peer-reviewed
Repository URI
Repository DOI
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
2168-8745
Volume Title
33
Publisher
Institute of Mathematical Statistics
Publisher DOI
Rights
All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/N031938/1)
Engineering and Physical Sciences Research Council (EP/P031447/1)
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.