正态线性模型中可估函数的极小极大估计(英文)On Minimax Estimators of Estimable Functions in Normal Linear Experiments
回钰
摘要(Abstract):
论述正态线形模型NL(Xβ,δ~2V),其中V为已知k×n正定矩阵,σ~2>0为未知参数,在二次损失|σ~2+β~TX~TV~1Xβ|~1||δ SXβ||下,根据可容许性理论,证明了SXβ的线性估计是其一切估计类中的唯一极小极大估计。
关键词(KeyWords): 正态线性模型;二次损失;可估线性函数,极小极大估计;可容许性理论
基金项目(Foundation):
作者(Author): 回钰
DOI: 10.16393/j.cnki.37-1436/z.2000.04.004
参考文献(References):
- [1] Khursheed A. A family of admissible minimax estimator of the mean of a multivariate normal distribution [J].Ann. Stat.,1979,(1) : 517~525
- [2] Baranchik A J. A family of minimax estimator of the mean of a multivariate normal distribution[J]. Ann. Math. Stat., 1970,41: 642~645
- [3] Efron B, Monts C. Families of minimax estimators of the mean of a multivariate normal distribution[J]. Ann. Stat., 1976,(4) : 11~21
- [4] 徐兴忠.二次损失下回归系数的线性估计[J].数学年刊,1993,14A,(5) :621~628
- [5] 陈希儒等.线性模型参数的估计理论[M].北京:科学出版社,1985