在线阅读 --自然科学版 2019年6期《带混合测量误差的线性回归模型的参数估计》
带混合测量误差的线性回归模型的参数估计--[在线阅读]
魏伟
天津大学 数学学院, 天津 300350
起止页码: 479--483页
DOI: 10.13763/j.cnki.jhebnu.nse.2019.06.005
摘要
在研究带测量误差的线性回归模型时常考虑的是classical测量误差或者Berkson测量误差,而classical和Berkson混合的测量误差研究较少.利用校正似然法讨论带classical和Berkson混合测量误差的线性回归模型的参数估计,并给出估计量的渐近分布.最后,通过R软件进行数值模拟验证估计方法的优良性.

Estimation of Linear Regression Models with Mixed Measurement Errors
WEI Wei
School of Mathematics, Tianjin University, Tianjin 300350, China
Abstract:
In the problem of linear regression models with measurement errors,classical measurement errors or Berkson measurement errors are often considered,but the mixture of classical and Berkson errors are less studied.The parameter estimation of linear regression models with mixed measurement errors is considered in this paper by using the corrected likelihood method,and the asymptotic distribution of the estimator is given.Finally,the numerical simulation in R is used to verify superiority of the estimation method.

收稿日期: 2019-04-15
基金项目:

参考文献:
[1]司小胜,胡昌华,周东华.带测量误差的非线性退化过程建模与剩余寿命估计[J].自动化学报,2013,39(5):530-541.doi:10.3724/sp.j.1004.2013.00530 SI Xiaosheng,HU Changhua,ZHOU Donghua.Nonlinear Degradation Process Modeling and Remaining Useful Life Estimation Subject to Measurement Error[J].Acta Automatica Sinica,2013,39(5):530-541.
[2]ADCOCK R J.Note on the Method of Least Squares[J].Analyst,1877,4(6):183-184.
[3]FULLER W A.Measurement Error Models[M].New York:Wiley,1987.doi:10.1002/9780470316665.fmatter
[4]CARROLL R J,RUPPERT D,CRAINICEANU C M,et al.Measurement Error in Nonlinear Models:A Modern Perspective[M].Boca Raton:Chapman and Hall/Crc,2006.
[5]YIN Z,GAO W,TANG M L,et al.Estimation of Nonparametric Regression Models with A Mixture of Berkson and Classical Errors[J].Statistics & Probability Letters,2013,83(4):1151-1162.doi:10.1016/j.spl.2013.01.013
[6]NAKAMURA T.Corrected Score Function for Errors-in-cariables Models:Methodology and Application to Generalized Linear Models[J].Biometrika,1990,77(1):127-137.doi:10.1093/biomet/77.1.127
[7]STEFANSKI L A,CARROLL R J.Conditional Scores and Optimal Scores for Generalized Linear Measurement-error Models[J].Biometrika,1987,74(4):703-716.doi:10.1093/biomet/74.4.703
[8]HUBER P J.Robust Statistics[M].New York:Wiley,1981.
[9]LIANG H,HÄRDLE W,CARROLL R J.Estimation in A Semiparametric Partially Linear Errors-in-variables Model[J].The Annals of Statistics,1999,27(5):1519-1535.doi:10.1214/aos/1017939140
[10]YANG Y P,LI G R,TONG T J.Corrected Empirical Likelihood for a Class of Generalized Linear Measurement Error Models[J].Science China Mathematics,2015,58(7):1523-1536.doi:10.1007/s11425-015-4976-6