Some Developments in the Theory of Shape Constrained Inference

Journal article (2018)

Authors

P. Groeneboom Statistics - EEMCS
G. Jongbloed Statistics - EEMCS
Research Group
Statistics (EEMCS) (TU Delft)
Copyright: © 2018 P. Groeneboom, G. Jongbloed
DOI
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https://doi.org/10.1214/18-STS657
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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Statistics

Abstract

Shape constraints enter in many statistical models. Sometimesthese constraints emerge naturally from the origin of the data. In other situations,they are used to replace parametric models by more versatile modelsretaining qualitative shape properties of the parametric model. In this paper,we sketch a part of the history of shape constrained statistical inference in anutshell, using landmark results obtained in this area. For this, we mainly usethe prototypical problems of estimating a decreasing probability density on [0,∞) and the estimation of a distribution function based on current statusdata as illustrations.

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