Estimations for some functions of covariance matrix in high dimension under non-normality and its applications
Estimations for some functions of covariance matrix in high dimension under non-normality and its applications
复制标题
非正态性下高维协方差矩阵某些函数的估计及其应用
DOI：
10.1016/j.jmva.2014.04.020
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发表时间：
2014
影响因子：
1.6
通讯作者：
T
中科院分区：
文献类型：
--
作者：
Himeno;T. and Yamada;T
当我们考虑高维情况下的统计检验时，我们经常需要协方差矩阵的函数的估计。特别地，需要估计a2 =（1/p）tr 2。当总体分布为多元正态分布时，a2的无偏相合估计已在前人的研究中提出。但在非正态情况下很难估计。在此基础上，我们给出了协方差阵中包含α 2的函数在非正态情况下的无偏相合估计。通过数值模拟，我们证实了我们提出的估计的近似精度。使用建议的估计，我们提出了一个测试评估多维正态性的高维数据。
When we consider a statistical test in the high dimensional case, we often need estimators of the functions of the covariance matrix Σ. Especially, it is needed to estimate a 2=(1/p) tr Σ 2. The unbiased and consistent estimator of a 2 is proposed in preceding study when the population distribution is multivariate normal. But it is difficult to estimate in the non-normal case. So we propose the unbiased and consistent estimators for some functions of covariance matrix including a 2 under the non-normal case. Through the numerical simulation, we confirmed the accuracy of the approximation of our proposed estimators. Using proposed estimators, we proposed a test for assessing multivariate normality of the high-dimensional data.