测量误差数据下线性模型的几乎无偏岭估计

周道清 邬吉波

摘 要 文章討论带测量误差的线性模型中参数估计的问题.当带测量误差的线性模型存在复共线的时候，通过几乎无偏估计的思想，提出了几乎无偏岭估计，并对估计的性质进行分析.通过研究发现几乎无偏岭估计不但能克服复共线性，同时有比较小的均方误差.

关键词 线性模型， 几乎无偏岭估计， 测量误差

中图分类号 O212文献标识码 A

Abstract We considered  parameter estimation in the linear model with measurement error. When linear model with measurement error exists multicollinearity， based on the idea of almost unbiased estimation， we proposed the almost unbiased ridge estimator in a linear model with measurement error. The property of the new estimator was also discussed. By  studying， we find that the new estimator not only can overcome multcollinearity but also has small mean squared error.

Key words linear regression model; almost unbiased ridge estimator; measurement error

3 结 论

文章首先利用几乎无偏估计的思想，提出一类新的几乎无偏岭估计来克服复共线性.同时发现在一定条件下新估计在均方误差意义下优于岭估计和最小二乘估计.

参考文献

[1]GLESER  L J. The importance of assessing measurement reliability in multivariate regression[J]. Journal of the American Statistical Association， 1992，419（87）：696-707.

[2] FULER  W A. Measurement error model[M].  New York：Wiley，1987.

[3] SALEH  A  K M E，SHALABH. A ridge regression estimation approach to the measurement error model[J]. Journal of Multivariate Analysis， 2014，123（1）： 68-84.

[4] HOERL  A E， KENNARD  R  W. Ridge regression： biased estimation for nonorthogonal problems[J].Technometrics，1970，12（1）：55-67.

[5] ZHONG Z， YANG H.Ridge estimation to the restricted linear model[J].Communications in Statistics-Theory and Methods， 2007，36（11）：2099-2115.

[6] LI  Y L，YANG H.On the performance of the jackknifed modified ridge estimator in the linear regression model with correlated or heteroscedastic errors[J]. Communications in Statistics-Theory and Methods， 2010，40（15）： 2695-2708.

[7] WU  J B， YANG  H.More on the unbiased ridge regression estimation[J]. Stat Papers，2017，57（1）：31-42.

[8] AKDENIZ  F， ROOZBEH M.Generalized difference-based weighted mixed almost unbiased ridge estimator in partially linear models[J].Statistical  Papers，2017（12）：1-23.