When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridg...When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.展开更多
In this paper,we propose a new biased estimator of the regression parameters,the generalized ridge and principal correlation estimator.We present its some properties and prove that it is superior to LSE(least squares ...In this paper,we propose a new biased estimator of the regression parameters,the generalized ridge and principal correlation estimator.We present its some properties and prove that it is superior to LSE(least squares estimator),principal correlation estimator,ridge and principal correlation estimator under MSE(mean squares error) and PMC(Pitman closeness) criterion,respectively.展开更多
基金The projects Supported by Natural Science Foundation of Fujian Province
文摘When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.
基金Foundation item： the National Natural Science Foundation of China （Nos. 60736047 10671007+2 种基金 60772036） the Foundation of Beijing Jiaotong University （Nos. 2006XM037 2007XM046）.
文摘In this paper,we propose a new biased estimator of the regression parameters,the generalized ridge and principal correlation estimator.We present its some properties and prove that it is superior to LSE(least squares estimator),principal correlation estimator,ridge and principal correlation estimator under MSE(mean squares error) and PMC(Pitman closeness) criterion,respectively.
