Estimation and Variable Selection for Semiparametric Additive Partial Linear Models (SS-09-140).
Estimation and Variable Selection for Semiparametric Additive Partial Linear Models (SS-09-140).
复制标题
DOI：
10.5705/ss.2009.140
复制
发表时间：
2011-07
影响因子：
1.4
通讯作者：
Liang H
中科院分区：
文献类型：
--
作者：
Liu X;Wang L;Liang H
半参数加性部分线性模型包含线性和非线性加性成分，与线性模型相比更灵活，与一般非参数回归模型相比更有效，因为它们减少了称为“维数灾难”的问题。在本文中，我们提出了一个新的估计方法，在这些模型中，我们使用多项式样条近似的加性非参数分量，我们得到的参数估计的渐近正态性。我们还开发了一个变量选择程序，以确定显着的线性成分使用平滑剪切绝对偏差惩罚（SCAD），我们表明，基于SCAD的估计的非零线性成分具有预言性质。模拟进行检查我们的方法相比，其他几个变量的选择方法，如贝叶斯信息准则和最小绝对收缩和选择算子（LASSO）的性能。所提出的方法也适用于营养流行病学研究的真实的数据，在该研究中，我们探讨了血浆β-胡萝卜素水平与个人特征（例如，年龄、性别、体重指数（BMI）等）以及饮食因素（例如，饮酒、吸烟状况、胆固醇摄入等）。
Semiparametric additive partial linear models, containing both linear and nonlinear additive components, are more flexible compared to linear models, and they are more efficient compared to general nonparametric regression models because they reduce the problem known as “curse of dimensionality”. In this paper, we propose a new estimation approach for these models, in which we use polynomial splines to approximate the additive nonparametric components and we derive the asymptotic normality for the resulting estimators of the parameters. We also develop a variable selection procedure to identify significant linear components using the smoothly clipped absolute deviation penalty (SCAD), and we show that the SCAD-based estimators of non-zero linear components have an oracle property. Simulations are performed to examine the performance of our approach as compared to several other variable selection methods such as the Bayesian Information Criterion and Least Absolute Shrinkage and Selection Operator (LASSO). The proposed approach is also applied to real data from a nutritional epidemiology study, in which we explore the relationship between plasma beta-carotene levels and personal characteristics (e.g., age, gender, body mass index (BMI), etc.) as well as dietary factors (e.g., alcohol consumption, smoking status, intake of cholesterol, etc.).
登录
查看更多内容
影响因子：
0.8
作者：
POLLARD, D
通讯作者：
POLLARD, D
影响因子：
1.6
作者：
Ni, Xiao;Zhang, Hao Helen;Zhang, Daowen
通讯作者：
Zhang, Daowen
DOI：
10.1111/j.1467-9868.2009.00718.x
发表时间：
2009-01-01
影响因子：
5.8
作者：
Ravikumar, Pradeep;Lafferty, John;Wasserman, Larry
通讯作者：
Wasserman, Larry
影响因子：
4.5
作者：
FOSTER, DP;GEORGE, EI
通讯作者：
GEORGE, EI
影响因子：
2.5
作者：
FRANK, IE;FRIEDMAN, JH
通讯作者：
FRIEDMAN, JH