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山东大学学报(理学版) ›› 2014, Vol. 49 ›› Issue (07): 69-74.doi: 10.6040/j.issn.1671-9352.0.2014.139

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线性误差协变量下部分线性模型的约束统计推断

赵培信1, 周小双2   

  1. 1. 河池学院数学与统计学院, 广西 宜州 546300;
    2. 德州学院数学科学学院, 山东 德州 253000
  • 收稿日期:2014-04-08 出版日期:2014-07-20 发布日期:2014-09-15
  • 作者简介:赵培信(1981- ),男,博士,教授,主要研究方向为非参数统计. E-mail:zpx81@163.com
  • 基金资助:
    国家自然科学基金资助项目(11101119);广西中青年优秀骨干教师培养工程资助项目

Restricted statistical inference for partially linear models with error-prone covariates

ZHAO Pei-xin1, ZHOU Xiao-shuang2   

  1. 1. College of Mathematics and Statistics, Hechi University, Yizhou 546300, Guangxi, China;
    2. College of Mathematics Sciences, Dezhou University, Dezhou 253000, Shandong, China
  • Received:2014-04-08 Online:2014-07-20 Published:2014-09-15

摘要: 考虑含有线性误差协变量部分线性模型的统计推断问题。对模型的参数分量,提出了一个线性约束条件下的最小二乘估计,并且证明该估计量满足渐近正态性。同时基于拉格朗日乘子检验方法对约束条件的合理性进行了检验。证明了所提出的检验统计量在原假设成立时渐近服从标准卡方分布。数据模拟表明所提出的估计方法可以有效地消除测量误差对估计精度的影响,并且所提出的检验方法对备择假设是相当敏感的。

关键词: 拉格朗日乘子检验, 部分线性模型, 线性误差协变量, 约束估计

Abstract: The statistical inference for the partially linear models with error-prone covariates were considered. A restricted least square estimation procedure of parametric components was proposed, and the resulting estimator was shown to be asymptotic normality. Moreover, a Lagrange multiplier testing method was proposed to test the validity of the linear restriction. It was proved that the proposed testing statistic follows an asymptotic standard Chi-square distribution under the null hypothesis. Simulation studies imply that the proposed estimation procedure can attenuate the effect of measurement errors, and the proposed testing method is more powerful.

Key words: error-prone covariates, restricted estimator, partially linear models, Lagrange multiplier test

中图分类号: 

  • O212.7
[1] XUE Liugen, ZHU Lixing. Empirical likelihood semiparametric regression analysis for longitudinal data[J]. Biometrika, 2007, 94:921-937.
[2] YANG Yiping, XUE Liugen, CHENG Weihu. Variable selection for partially linear models with randomly censored data[J]. Communications in Statistics-Simulation and Computation, 2010, 39:1577-1589.
[3] ZHOU Yong, LIANG Hua. Statistical inference for semi-parametric varying-coefficient partially models with error-prone linear covariates[J]. The Annals of Statistics, 2009, 37:427-458.
[4] LI Xiaoli, YOU Jinhong, ZHOU Yong. Statistical inference for varying-coefficient models with error-prone covariates[J]. Journal of Statistical Computation and Simulation, 2011, 81:1-17.
[5] ZHAO Peixin, XUE Liugen. Instrumental variable-based empirical likelihood inferences for varying-coefficient models with error-prone covariates[J]. Journal of Applied Statistics, 2013, 40:380-396.
[6] SHALABH, GARG G, MISRA N. Restricted regression estimation in measurement error models[J]. Computational Statistics & Data Analysis, 2007, 52:1149-1166.
[7] ZHANG Weiwei,LI Gaorong, XUE Liugen. Profile inference on partially linear varying-coefficient errors-in-variables models under restricted condition[J]. Computational Statistics & Data Analysis, 2011, 55: 3027-3040.
[8] WEI Chuanhua. Statistical inference for restricted partially linear varying coefficient errors-in-variables models [J]. Journal of Statistical Planning and Inference, 2012, 142:2464-2472.
[9] 魏传华, 吴喜之. 部分线性变系数模型的 Profile Lagrange 乘子检验[J]. 系统科学与数学, 2008, 28(4):416-424. WEI Chuanhua, WU Xizhi. Profile Lagrange multiplier test for partially linear varying-coefficient regression models[J]. Journal of Systems Science and Complexity, 2008, 28(4): 416-424.
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