測量誤差數據下線性模型的幾乎無偏嶺估計

周道清 鄔吉波

摘 要 文章討論帶測量誤差的線性模型中參數估計的問題.當帶測量誤差的線性模型存在復共線的時候，通過幾乎無偏估計的思想，提出了幾乎無偏嶺估計，并對估計的性質進行分析.通過研究發現幾乎無偏嶺估計不但能克服復共線性，同時有比較小的均方誤差.

關鍵詞 線性模型， 幾乎無偏嶺估計， 測量誤差

中圖分類號 O212文獻標識碼 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 結 論

文章首先利用幾乎無偏估計的思想，提出一類新的幾乎無偏嶺估計來克服復共線性.同時發現在一定條件下新估計在均方誤差意義下優于嶺估計和最小二乘估計.

參考文獻

[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.