Functional Linear Model with Zero-value Coefficient Function at Sub-regions.
Functional Linear Model with Zero-value Coefficient Function at Sub-regions.
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DOI：
10.5705/ss.2010.237
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发表时间：
2013-01-01
影响因子：
1.4
通讯作者：
Wang N
中科院分区：
文献类型：
--
作者：
Zhou J;Wang NY;Wang N
提出了一种收缩方法来估计泛函线性回归模型中系数函数在某些子区域内为零的情况。除了确定空区域中的系数函数为零，我们还旨在进行估计和推断的非参数估计系数函数，而不会过度收缩的值。我们的建议包括两个阶段。在第一阶段，Dantzig选择器被用来提供零区域的初始位置。在第二阶段，我们提出了一个组SCAD方法来细化零区域的估计位置，并提供系数函数的估计和推断过程。我们的考虑在这种功能设置中具有某些优势。一个目标是减少模型中使用的参数数量。对于一个阶段的程序，它需要使用大量的节点，以精确地识别零系数区域，然而，随着参数的数量的变化和估计的难度增加。由于额外的细化阶段，我们避免了这种必要性，我们的估计在实践中实现了上级的数值性能。我们发现，我们的估计享有Oracle属性，它确定的零区域的概率趋于1，它实现了相同的渐近正态性的估计系数函数的非零区域时，非零区域是已知的功能线性模型估计。在数值上，我们的改进估计克服了初始Dantzig估计的缺点，往往低估了非零系数的绝对规模。所提出的方法的性能在仿真研究中示出。我们应用的方法在分析收集的数据由约翰霍普金斯先驱研究，其中的主要利益是在估计的强度之间的关联在中年的身体质量指数和生活质量的身体功能在老年，并在确定有效的年龄范围内存在这种协会。
We propose a shrinkage method to estimate the coefficient function in a functional linear regression model when the value of the coefficient function is zero within certain sub-regions. Besides identifying the null region in which the coefficient function is zero, we also aim to perform estimation and inferences for the nonparametrically estimated coefficient function without over-shrinking the values. Our proposal consists of two stages. In stage one, the Dantzig selector is employed to provide initial location of the null region. In stage two, we propose a group SCAD approach to refine the estimated location of the null region and to provide the estimation and inference procedures for the coefficient function. Our considerations have certain advantages in this functional setup. One goal is to reduce the number of parameters employed in the model. With a one-stage procedure, it is needed to use a large number of knots in order to precisely identify the zero-coefficient region; however, the variation and estimation difficulties increase with the number of parameters. Owing to the additional refinement stage, we avoid this necessity and our estimator achieves superior numerical performance in practice. We show that our estimator enjoys the Oracle property; it identifies the null region with probability tending to 1, and it achieves the same asymptotic normality for the estimated coefficient function on the non-null region as the functional linear model estimator when the non-null region is known. Numerically, our refined estimator overcomes the shortcomings of the initial Dantzig estimator which tends to under-estimate the absolute scale of non-zero coefficients. The performance of the proposed method is illustrated in simulation studies. We apply the method in an analysis of data collected by the Johns Hopkins Precursors Study, where the primary interests are in estimating the strength of association between body mass index in midlife and the quality of life in physical functioning at old age, and in identifying the effective age ranges where such associations exist.
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影响因子：
2.7
作者：
Wang, Hansheng;Li, Runze;Tsai, Chih-Ling
通讯作者：
Tsai, Chih-Ling
影响因子：
4.5
作者：
Zou, Hui;Li, Runze
通讯作者：
Li, Runze
影响因子：
1.1
作者：
Lounici, Karim
通讯作者：
Lounici, Karim
影响因子：
4.5
作者：
Fan, JQ;Peng, H
通讯作者：
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DOI：
10.1111/j.1467-9868.2008.00668.x
发表时间：
2009-01-01
影响因子：
5.8
作者：
James, Gareth M.;Radchenko, Peter;Lv, Jinchi
通讯作者：
Lv, Jinchi