Influential observations in the estimation of mean vector and covariance matrix.
Influential observations in the estimation of mean vector and covariance matrix.
复制标题
对均值向量和协方差矩阵的估计有影响的观察结果。
DOI：
--
复制
发表时间：
2002
影响因子：
2.6
通讯作者：
Y. Poon
中科院分区：
文献类型：
--
作者：
W. Poon;Y. Poon
为分析多变量数据集而设计的统计程序通常强调不同的样本统计数据。虽然某些程序强调平均向量 mu 和协方差矩阵 Sigma 的估计，但其他程序可能仅强调这两个样本量之一。实际上，虽然数据集中的异常观察会对严重依赖协方差矩阵的分析结果产生有害影响，但当依赖于均值向量时，其影响可能很小。本文的目的是制定诊断措施来识别不同类型的有影响力的观察结果。构建了基于局部影响方法的三种诊断措施，以识别对 Sigma 的 mu 估计值以及两者的估计值产生不当影响的观察结果。分析真实数据集并提供结果以说明所提出措施的有效性。
Statistical procedures designed for analysing multivariate data sets often emphasize different sample statistics. While some procedures emphasize the estimates of both the mean vector mu and the covariance matrix Sigma, others may emphasize only one of these two sample quantities. In effect, while an unusual observation in a data set has a deleterious impact on the results from an analysis that depends heavily on the covariance matrix, its effect when dependence is on the mean vector may be minimal. The aim of this paper is to develop diagnostic measures for identifying influential observations of different kinds. Three diagnostic measures, based on the local influence approach, are constructed to identify observations that exercise undue influence on the estimate of mu of Sigma, and of both together. Real data sets are analysed and results are presented to illustrate the effectiveness of the proposed measures.