有缺失数据的条件独立正态母体中参数的最优同变估计

许凯, 何道江

数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 783-794.

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数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 783-794. DOI: 10.12386/A2016sxxb0070
论文

有缺失数据的条件独立正态母体中参数的最优同变估计

    许凯1, 何道江2
作者信息 +

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

    Kai XU1, Dao Jiang HE2
Author information +
文章历史 +

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.

Abstract

Under the assumption that the missing data mechanism is ignorable, we derive the maximum likelihood and unbiased estimators of the Cholesky decomposition of covariance and precision matrices in a conditional independent normal model with monotone 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

Key words

Cholesky decomposition / equivariant estimator / invariant Haar measure

引用本文

导出引用
许凯, 何道江. 有缺失数据的条件独立正态母体中参数的最优同变估计. 数学学报, 2016, 59(6): 783-794 https://doi.org/10.12386/A2016sxxb0070
Kai XU, Dao Jiang HE. The Best Equivariant Estimator of the Parameters in a Conditional Independent Normal Distribution with Missing Data. Acta Mathematica Sinica, Chinese Series, 2016, 59(6): 783-794 https://doi.org/10.12386/A2016sxxb0070

参考文献

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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)

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