部分线性可加模型的随机约束岭估计
A Stochastic Restricted Ridge Estimator in Partially Linear Additive Models
DOI: 10.12677/SA.2022.116151, PDF,    科研立项经费支持
作者: 李 静：中国劳动关系学院应用技术学院，北京；李雪艳：中国民航大学理学院，天津；安佰玲：淮北师范大学数学科学学院，安徽 淮北
关键词: 部分线性可加模型；随机线性约束；Profile最小二乘估计；岭估计；Partially Linear Additive Model； Stochastic Linear Restriction； Profile Least Squares Approach； Ridge Estimation
摘要: 本文研究了部分线性可加模型这类半参数模型在线性部分自变量存在多重共线性，同时还附加有随机约束条件时的估计问题。基于针对半参数模型的Profile最小二乘技术，处理多重共线性问题的岭估计方法以及针对随机约束的混合估计技术，构造了参数分量的随机约束岭估计，给出了估计量的偏与协方差，并给出了所提估计量的渐近性质。最后通过数值模拟验证了所提估计方法的表现。
Abstract: This paper studies the estimation of a partially linear additive model when there are stochastic linear restrictions on the parameter components and multicollinearity problem exists, simultaneously. Based on the profile least square method of semiparametric model, ridge estimation approach for multicollinearity problem and mixed estimation technique for stochastic restrictions, a stochastic ridge estimator for the parametric components was proposed and its bias and covariance were provided. Meanwhile, the asymptotic distribution of this proposed estimator has also been proved. Finally, some simulations are carried out to study the finite properties of the proposed estimator.
文章引用：李静, 李雪艳, 安佰玲. 部分线性可加模型的随机约束岭估计[J]. 统计学与应用, 2022, 11(6): 1448-1455. https://doi.org/10.12677/SA.2022.116151

参考文献

[1] Opsomer, J.D. and Ruppert, D. (1999) A Root-n Consistent Backfitting Estimator for Semiparametric Additive Modeling. Journal of Computational and Graphical Statistics, 8, 715-732.
[Google Scholar] [CrossRef] 
[2] Manzana, S. and Zeromb, D. (2005) Kernel Estimation of a Partially Linear Additive Model. Statistics & Probability Letters, 72, 313-322.
[Google Scholar] [CrossRef] 
[3] Liu, X., Wang, L. and Liang, H. (2011) Estimation and Variable Selection for Semiparametric Additive Partial Linear Model. Statistica Sinica, 21, 1225-1248.
[Google Scholar] [CrossRef] [PubMed]
[4] Wei, C.H. and Liu, C.L. (2012) Statistical Inference on Semiparametric Partially Linear Additive Models. Journal of Nonparametric Statistic, 24, 809-823.
[Google Scholar] [CrossRef] 
[5] Liu, K.J. (2003) Using Liu-Type Estimator to Combat Collinearity. Communcation in Statistics-Theory and Methods, 32, 285-292.
[Google Scholar] [CrossRef] 
[6] Wei, C.H. and Wang, X.N. (2016) Liu-Type Estimator in Semiparametric Partially Linear Additive Models. Journal of Nonparametric Statistics, 28, 459-468.
[Google Scholar] [CrossRef] 
[7] Wei, C.-H. (2016) A Stochastic Restricted Estimator in Partially Linear Additive Models. Far East Journal of Theoretical Statistics, 52, 35-477.
[Google Scholar] [CrossRef] 
[8] 王肖南, 魏传华. 部分线性可加模型的随机约束Liu估计[J]. 中央民族大学学报(自然科学版), 2016, 25(1): 80-85.
[9] 蓝文英. 部分线性可加模型基于backfitting方法的岭估计[J]. 中央民族大学学报(自然科学版), 2013, 22(S1): 68-71.
[10] Özkale, M.R. (2009) A Stochastic Restricted Ridge Regression Estimator. Journal of Multivariate Analysis, 100, 1706- 1716.
[Google Scholar] [CrossRef] 
[11] 魏传华, 郭双, 王肖南. 部分线性模型的随机约束岭估计[J]. 数学的实践与认识, 2014, 44(13): 249-254.
[12] 刘超, 韦杰, 魏传华. 部分线性变系数模型的随机约束岭估计[J]. 应用数学, 2017, 30(4): 774-779.
[13] Opsomer, J.D. and Ruppert, D. (1997) Fitting a Bivariate Additive Model by Local Polynomial Regression. The Annals of Statistics, 25, 186-211.
[Google Scholar] [CrossRef] 
[14] Rao, C.R., Shalabh, Toutenburg, H. and Heumann, C. (2008) Linear Models and Generalization: Least Squares and Alternatives. Springer, Berlin.
[15] McDonald, G.C. and Galarneau, D.I. (1975) A Monte Carlo Evaluation of Some Ridge-Type Estimators. Journal of American Statistical Association, 70, 407-416.
[Google Scholar] [CrossRef] 

为你推荐