周道清 鄔吉波

摘 要 文章討論帶測(cè)量誤差的線性模型中參數(shù)估計(jì)的問(wèn)題.當(dāng)帶測(cè)量誤差的線性模型存在復(fù)共線的時(shí)候，通過(guò)幾乎無(wú)偏估計(jì)的思想，提出了幾乎無(wú)偏嶺估計(jì)，并對(duì)估計(jì)的性質(zhì)進(jìn)行分析.通過(guò)研究發(fā)現(xiàn)幾乎無(wú)偏嶺估計(jì)不但能克服復(fù)共線性，同時(shí)有比較小的均方誤差.

關(guān)鍵詞 線性模型， 幾乎無(wú)偏嶺估計(jì)， 測(cè)量誤差

中圖分類號(hào) O212文獻(xiàn)標(biāo)識(shí)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(jié) 論

文章首先利用幾乎無(wú)偏估計(jì)的思想，提出一類新的幾乎無(wú)偏嶺估計(jì)來(lái)克服復(fù)共線性.同時(shí)發(fā)現(xiàn)在一定條件下新估計(jì)在均方誤差意義下優(yōu)于嶺估計(jì)和最小二乘估計(jì).

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