重庆工商大学学报：自然科学版
重慶工商大學學報：自然科學版
중경공상대학학보：자연과학판
Journal of Chongqing Technology and Business University:Natural Science Edition
2012年
3期
7-11
,共5页
Liu型估计%约束最小二乘估计%均方误差%均方误差矩阵
Liu型估計%約束最小二乘估計%均方誤差%均方誤差矩陣
Liu형고계%약속최소이승고계%균방오차%균방오차구진
Liu-type Estimator%restricted least square estimator%mean square error%mean square error matrix
考虑带等式约束的奇异线性模型的参数估计，为了克服复共线性问题，提出一个新的Liu型估计；同时给出这个估计的一些性质，并且得到了这个新的Liu型估计在均方误差矩阵准则（MSEM）下优于约束最小二乘估计的充要条件；得到在均方误差（MSE）准则下新估计优于约束最小二乘估计的充分条件．
攷慮帶等式約束的奇異線性模型的參數估計，為瞭剋服複共線性問題，提齣一箇新的Liu型估計；同時給齣這箇估計的一些性質，併且得到瞭這箇新的Liu型估計在均方誤差矩陣準則（MSEM）下優于約束最小二乘估計的充要條件；得到在均方誤差（MSE）準則下新估計優于約束最小二乘估計的充分條件．
고필대등식약속적기이선성모형적삼수고계，위료극복복공선성문제，제출일개신적Liu형고계；동시급출저개고계적일사성질，병차득도료저개신적Liu형고계재균방오차구진준칙（MSEM）하우우약속최소이승고계적충요조건；득도재균방오차（MSE）준칙하신고계우우약속최소이승고계적충분조건．
This paper considers parameter estimator on singular linear model with equation restriction, presents a new Liu-type Estimator in order to overcome collinearity, gives some properties for this Estimator, obtains the sufficient and necessary condition for this new Liu-type Estimator superior to restricted least square estimator under mean square error matrix criterion and also receives sufficient condition for the new Estimator superior to restricted least square estimator in terms of mean square error criterion.
