缺失数据下线性模型回归系数岭估计的大样本性质.pdfVIP

: seen in Wang etal. (Theory and Application of the Linear Model [M]. Hefei, Anhui Education Press, 1987; Introduction to Linear Model[M]. Beijing: Higher Education Press, 2004.), which gave a series of sufficient conditions that ridge estimation is superior to LSE. Dai (The conditions that ridge estimation is superior to least square estimation[J]. Mathematical Statistics and Applied Probability, 1994, 9(2): 53-58.) discussed the problem for the superiority of ridge estimation over LSE in the sense of mean square error. He obtained same necessary conditions under which ridge estimate is superior to LSE. Wang (The consistency of ridge regression [J]. Mathematical Statis- tics and Applied Probability, 1987, 3(1): 42-51.) discussed the consistency of ridge regression, some limit properties of estimates of error variance based on the ridge regression and proved that it shares the same properties with LSE. Many researchers proposed some improved ridge estimates in order to improve the accuracy of the estimates in terms of the mean square error. In a linear model with equality restrictions, as Zheng (Restricted linear estimations[J]. Chi- nese Journal of Applied Probability and Statistics, 1986, 2(1): 5-12.) said, the mean square error of , the restricted LSE of , may be larger under certain conditions, which leads to unsatisfactory results. It made people to find a class of reasonable estimators to improve from the biased esti- mators of . Lei (Convergence of the ridge estimations of the linear model[J]. Journal of Guangxi Normal University, 1999, 10(1): 21-24.) studied the strong convergence, weak convergence and mean square convergence of the ridge regression in a linear model with the restriction , and obtained the necessary and sufficient conditions for weak convergence and sufficient condi- tions for strong convergence. Shi (The conditional ridge-type estimation of regr