Shape constrained estimation: Theory and methods

形状约束估计：理论与方法

• 批准号: 342858-2013
• 负责人: Jankowski, Hanna
• 金额: $ 1.09万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=595605
• 关键词: Shape; constrained; estimation; Theory; methods

Estimation of a function lies at the core of much of current statistical methodology. There are two main competing methods here: parametric and nonparametric estimation. Parametric methodology is simple, efficient, well-understood, but may not be robust. Nonparametric methods are more robust, and therefore preferable for medium to large sample sizes. Kernel-based estimators are one popular class of nonparametric methods, but these require the user to select a bandwidth, which is difficult to do optimally. An alternative nonparametric approach, called shape-constrained estimation, is an important and highly attractive option.

函数的估计是当前许多统计方法的核心。这里有两种主要的竞争方法：参数估计和非参数估计。参数化方法简单、有效、易于理解，但可能不够稳健。非参数方法更稳健，因此更适合中大型样本量。基于核的估计器是一类流行的非参数方法，但这些方法需要用户选择带宽，这很难做到最优。另一种非参数方法，称为形状约束估计，是一种重要且非常有吸引力的选择。