Some Developments in the Theory of Shape Constrained Inference
Some Developments in the Theory of Shape Constrained Inference
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DOI：
10.1214/18-sts657
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发表时间：
2018-11-01
影响因子：
5.7
通讯作者：
Jongbloed, Geurt
中科院分区：
文献类型：
--
作者：
Groeneboom, Piet;Jongbloed, Geurt
形状约束出现在许多统计模型中。有时，这些约束从数据的起源中自然出现。在其他情况下，它们被用来用更通用的模型代替参数模型，保留参数模型的定性形状属性。在本文中，我们简要概述了形状约束统计推断的一部分历史，使用在该领域获得的里程碑式的结果。为此，我们主要使用[0，无穷大]上估计递减概率密度的原型问题和基于当前状态数据估计分布函数的原型问题作为说明。
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, infinity) and the estimation of a distribution function based on current status data as illustrations.