Statistical Science

Some Developments in the Theory of Shape Constrained Inference

Piet Groeneboom and Geurt Jongbloed

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

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Statist. Sci., Volume 33, Number 4 (2018), 473-492.

First available in Project Euclid: 29 November 2018

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Isotonic regression Grenander estimator inverse problem monotonicity interval censoring current status regression single index model bootstrap Chernoff’s distribution Airy functions


Groeneboom, Piet; Jongbloed, Geurt. Some Developments in the Theory of Shape Constrained Inference. Statist. Sci. 33 (2018), no. 4, 473--492. doi:10.1214/18-STS657.

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