Semi-parametric additive constrained regression

被引:31
|
作者
Meyer, Mary C. [1 ]
机构
[1] Colorado State Univ, Dept Stat, Ft Collins, CO 80523 USA
基金
美国国家科学基金会;
关键词
cone projection; multiple isotonic regression; degrees of freedom; variable selection; (E)over-bar(01) test; ALGORITHM; FREEDOM; MODEL;
D O I
10.1080/10485252.2013.797577
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
The additive isotonic least-squares regression model has been fit using a sequential pooled adjacent violators algorithm, estimating each isotonic component in turn, and looping until convergence. However, the individual components are not, in general, estimable. The sum of the components, i.e. the expected value of the response, has a unique estimate, which can be found using a single cone projection. Estimators for the individual components are then easily obtained, which are unique if the conditions for estimability hold. Parametrically modelled covariates are easily included in the cone projection specification. The cone structure also provides information about the degrees of freedom of the fit, which can be used in inference methods, variable selection, and estimation of the model variance. Simulations show that these methods can compare favourably to standard parametric methods, even when the parametric assumptions are correct. The estimation and inference methods can be extended to other constraints such as convex regression or isotonic regression on partial orderings.
引用
收藏
页码:715 / 730
页数:16
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