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November 2018 Some Developments in the Theory of Shape Constrained Inference
Piet Groeneboom, Geurt Jongbloed
Statist. Sci. 33(4): 473-492 (November 2018). DOI: 10.1214/18-STS657


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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Piet Groeneboom. Geurt Jongbloed. "Some Developments in the Theory of Shape Constrained Inference." Statist. Sci. 33 (4) 473 - 492, November 2018.


Published: November 2018
First available in Project Euclid: 29 November 2018

zbMATH: 07032825
MathSciNet: MR3881204
Digital Object Identifier: 10.1214/18-STS657

Keywords: Airy functions , bootstrap , Chernoff’s distribution , current status regression , Grenander estimator , interval censoring , inverse problem , isotonic regression , Monotonicity , Single index model

Rights: Copyright © 2018 Institute of Mathematical Statistics


Vol.33 • No. 4 • November 2018
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