部分线性变系数模型的Liu估计

doi:10.13438/j.cnki.jdzk.2022.04.001

吉首大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (4): 1-6.DOI: 10.13438/j.cnki.jdzk.2022.04.001

• 数学 • 下一篇

部分线性变系数模型的Liu估计

安佰玲,卢琦,马宁

(淮北师范大学数学科学学院,安徽淮北 235000)

出版日期:2022-07-25 发布日期:2022-10-28
作者简介:安佰玲（1977—），女，山东日照人，淮北师范大学数学科学学院副教授，硕士，主要从事概率论与数理统计学研究.
基金资助:
安徽省高等学校自然科学研究项目（KJ2020A1200，KJ2019A0956）；淮北师范大学质量工程项目（2021XJXYJ023）

Liu Estimation in Partially Linear Varying Coefficient Models

AN Bailing,LU Qi,MA Ning

(School of Mathematics,Huaibei Normal University,Huaibei 235000,Anhui China)

Online:2022-07-25 Published:2022-10-28

摘要/Abstract

摘要：研究了部分线性变系数模型中参数分量的有偏估计问题.基于Profile最小二乘方法和Liu估计法构造了参数分量的Profile-Liu估计和剖面最小二乘广义Liu估计，并在一定的条件下，证明了Profile-Liu估计优于Profile最小二乘估计，剖面最小二乘广义Liu估计优于Profile-Liu估计.

关键词： 部分线性变系数模型, Liu估计, Profile最小二乘方法, 多重共线性

Abstract: This paper considers the biased estimators on the parameter components in partially linear varying coefficient model.Based on the Profile least-square approach and Liu estimation method,we propose Profile-Liu estimator and section least-square general Liu estimator for the parametric components.We prove that the Profile-Liu estimation is better than the Profile least-square estimation,and the section least-square general Liu estimation is better than the Profile-Liu estimation under certain conditions.

Key words: partially linear varying coefficient model, Liu estimation, Profile least-squares approach, multicollinearity

安佰玲, 卢琦, 马宁. 部分线性变系数模型的Liu估计[J]. 吉首大学学报（自然科学版）, 2022, 43(4): 1-6.

AN Bailing, LU Qi, MA Ning. Liu Estimation in Partially Linear Varying Coefficient Models[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(4): 1-6.

参考文献

[1] ZHANG Wenyang,LEE SIK-YUM,SONG Xinyuan.Local Polynomial Fitting in Semi-Varying Coefficient Models[J].Journal of Multivariate Analysis,2002,82(1):166-188.
[2] XIA Yingcun,ZHANG Wenyang,TONG HOWELL.Efficient Estimation for Semivarying-Coefficient Models[J].Biometrika,2004,91(3):661-681.
[3] ZHOU Xian,YOU Jinhong.Wavelet Estimation in Varying-Coefficient Partially Linear Model[J].Statistical & Probability Letter,2004,68(1):91-104.
[4] FAN Jianqing,HUANG Tao.Profile Likelihood Inferences on Semi-Parametric Varying-Coefficient Partially Linear Models[J].Bernoulli,2005,11(6):1031-1057.
[5] WEI Chuanhua,LIU Chunling.Statistical Inference on Semiparametric Partially Linear Additive Model[J].Journal of Nonparametric Statistic,2012,24(4):809-823.
[6] LIU Kejian.A New Class of Some Biased Regression Estimators[J].Communication in Statistics-Theory and Methods,1993,22(2):393-402.
[7] AKDENIZ FIKRI,DURAN ESRA AKDENIZ.Liu-Type Estimator in Semiparametric Regression Models[J].Journal of Statistical Computation and Simulation,2010,80(8):853-871.
[8] DURAN ESRA AKDENIZ,AKDENIZ FIKRI,HU Hongchang.Efficiency of a Liu-Type Estimator in Semiparametric Regression Models[J].Journal of Computational and Applied Mathematics,2011,235(5):1418-1428.
[9] WEI Chuanhuan,WANG Xiaonan.Liu-Type Estimator in Semiparametric Partially Linear Additive Model[J].Journal of Nonparametric Statistic,2016,28(3):459-468.
[10] 梅长林，王宁.近代回归分析方法[M].北京：科学出版社，2012:40.
[11] 王松桂,陈敏,陈丽萍.线性统计模型[M].北京：高等教育出版社,1999:59.
[12] HOERL ARTHUR E,KENNARD ROBERT W.Ridge Regression Biased Estimation for Nonorthogonal Problems[J].Tecchnometrics,1970,12(1):55-67.
[13] AKDENIZ FIKRI,KACIRANLAR SELAHATTIN.On the Almost Unbiased Generalized Liu Estimator and Unbiased Estimation of the Bias and MSE[J].Communication in Statistics-Theory and Methods,1995,24(7):1789-1797.
[14] 王肖南,魏传华.参数可加模型的Liu估计[J].统计与决策，2015(8)：28-30.
[15] 韦杰.部分线性变系数模型的约束岭估计[J].产业与科技论坛，2016,15(7)：87-89.

部分线性变系数模型的Liu估计

Liu Estimation in Partially Linear Varying Coefficient Models

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