有缺失数据的条件独立正态母体中参数的最优同变估计  

The Best Equivariant Estimator of the Parameters in a Conditional Independent Normal Distribution with Missing Data

作　　者：许凯[1] 何道江[2] 

机构地区：[1]上海财经大学统计与管理学院,上海200433 [2]安徽师范大学数学计算机科学学院,芜湖241000

出　　处：《数学学报（中文版）》2016年第6期783-794,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11201005);全国统计科学研究计划重点项目(2013LZ17);安徽省自然科学基金(1308085QA13);上海财经大学研究生创新基金(CXJJ-2015-440)

摘　　要：在缺失数据机制是可忽略的假设下,导出了有单调缺失数据的条件独立正态模型中协方差阵和精度阵的Cholesky分解的最大似然估计和无偏估计.通过引入一类特殊的变换群并在更广义的损失下,获得了其最优同变估计.这表明最大似然估计和无偏估计是非容许的.最后,通过数值模拟验证了相关结果的有效性.Under the assumption that the missing data mechanism is ignorable, we derive the maximmn likelihood and unbiased estimators of the Cholesky decomposition of covariance and precision matrices in a conditional independent normal model withmonotone missing data. By introducing a special group, we obtain the best equivariant estimators under more generalized losses, which implies that the maximum likelihood and unbiased estimators are all inadmissible. Finally, some simulations are given to examine the performance of the relevant results.

关 键 词：CHOLESKY分解 同变估计 不变Haar测度 

分 类 号：O212.2[理学—概率论与数理统计]