部分线性模型的LASSO估计及其渐近性

J4 ›› 2012, Vol. 47 ›› Issue (3): 93-97.

部分线性模型的LASSO估计及其渐近性

李锋¹,卢一强²

1. 郑州航空工业管理学院经贸学院，河南郑州 450015;
2. 中国人民解放军信息工程大学电子技术学院，河南郑州 450004

收稿日期:2011-04-10 出版日期:2012-03-20 发布日期:2012-04-01
作者简介:李锋（1978- ），男，讲师，博士，研究方向为非参、半参数统计，高维降维。Email:lifengsta@gmail.com

Asymptotics for the LASSO estimator for partially linear models

LI Feng1, LU Yi-qiang2

1. Resource & Economic Trade Department, Zhengzhou Institute of Aeronautical Industry Management,
Zhengzhou 450015, Henan, China;
2. Institute of Electronic Technology, The PLA Information Engineering University, Zhengzhou 450004, Henan, China

Received:2011-04-10 Online:2012-03-20 Published:2012-04-01

摘要/Abstract

摘要：

结合截面最小二乘估计思想，构造了LASSO惩罚截面最小二乘估计，并研究了惩罚参数和窗宽的选择问题。由于部分线性模型LASSO解仍为线性优化问题，因此容易实现。在一定条件下，本文还研究了参数估计量的相合性和渐近正态性。最后通过蒙特卡洛模拟研究了变量选择方法的小样本性质。

关键词: 部分线性模型；变量选择；渐近分布；LASSO

Abstract:

Based on the profile least squares method, the LASSO penalty profile least squares estimator is constructed, and the choices of penalty parameter and bandwidth are also discussed. Because the optimization problem is linear, it can be easily implemented. Under some regular conditions, the consistency and asymptotic normality of the estimator for parameter component are investigated. Finally, Monte Carlo simulation studies are conducted to assess the finite sample performance of the proposed variable selection procedures.

Key words: partially linear models; variable selection; asymptotics; LASSO

李锋1,卢一强2. 部分线性模型的LASSO估计及其渐近性[J]. J4, 2012, 47(3): 93-97.

LI Feng1, LU Yi-qiang2. Asymptotics for the LASSO estimator for partially linear models[J]. J4, 2012, 47(3): 93-97.

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