Stability of principal components |
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Authors: | A H Al-Ibrahim Noriah M Al-Kandari |
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Institution: | (1) Department of Statistics and OR, Kuwait University, P. O. Box 5696, Safat, 13060, Kuwait |
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Abstract: | 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.
This work was sponsored by a grant from the Office of Vice-President for Research at Kuwait University under project number
SS049. |
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Keywords: | Principal components Stability measure Maximum likelihood estimator Eigenvalue and eigenvector Coverage probability Stability confidence level |
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