摘要
考虑误差为正态分布的线性回归模型,通过利用附加伪观测数据模型的最小二乘估计与岭估计的关系,得到了基于岭估计的未知参数的最小体积置信集(区间或区域)。与经典置信集相比较,在最小体积意义下我们所得到的置信集是最佳的。最后给出了一个算例,结果表明所得的置信集比经典置信集更精确体积更小。
This studys selects linear regression models with a normal distribution of errors and uses the relation between the least squares estimation and the ridge estimation of the additional pseudo-observational data model,to calculate the minimum volume confidence sets(intervals or regions)of unknown parameters based on ridge estimate.Compared with the classical confidence sets,the confidence sets gained on the basis of minimum volume is the best.Finally,it also gives some model examples,the results of which show that the confidence sets obtained in this study is more accurate and smaller in volume than the classical confidence sets.
作者
胡宏昌
郭童格
HU Hongchang;GUO Tongge(School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)
出处
《湖北师范大学学报（自然科学版）》
2024年第1期16-22,共7页
Journal of Hubei Normal University：Natural Science
关键词
岭估计
线性回归
置信集
估计效率
ridge estimation
linear regression
confidence set
estimation efficiency
