Stability of principal components

被引:2
|
作者
Al-Ibrahim, A. H. [1 ]
Al-Kandari, Noriah M. [1 ]
机构
[1] Kuwait Univ, Dept Stat & OR, Safat 13060, Kuwait
关键词
principal components; stability measure; maximum likelihood estimator; eigenvalue and eigenvector; coverage probability; stability confidence level;
D O I
10.1007/s00180-007-0082-8
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In this article we deal with the problem of stability of the conclusions from principal components analysis over repeated samples. We define a measure of stability for each component and investigate some of the measures properties. We then obtain the maximum likelihood estimators (MLEs) of the measures, and derive their joint limiting distributions. The MLEs of the measures turn out to be asymptotically unbiased and jointly have the multivariate normal distribution. Modified estimators are also found to reduce the amount of bias in the MLEs. To facilitate interpretation of the measures we define stability confidence level as coverage probability, and associate with each measure a stability confidence level to describe the measure in terms of probability. Finally, we investigate the stability of the components via a simulation study and compare the performance of the MLEs and the modified estimators in terms of bias and precision.
引用
收藏
页码:153 / 171
页数:19
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