JSM 2005 Online Program

Abstract #302817

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Activity Number:	35
Type:	Contributed
Date/Time:	Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor:	General Methodology
Abstract - #302817
Title:	Stability of the Principal Components
Author(s):	Abdul-Hamid Al-Ibrahim*+
Companies:	Kuwait University
Address:	PO Box 5969, Safat, 13060, Kuwait
Keywords:	principal components analysis ; stability measure ; maximum likelihood estimator ; eigenvalue and eigenvector ; coverage probability
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 measure's properties. We then obtain the maximum likelihood estimator (MLE) of the measures and derive their joint limiting distribution. The MLE estimators of the measures turn out to be asymptotically unbiased and jointly have the multivariate normal distribution. Modified estimators are defined in the hope of reducing bias in the case of small sample sizes. We compare performance of the estimators in terms of bias and stability via a simulation study. Generally, the simulation results indicate the measures of the first two components are stable provided the ratio of successive eigenvalues is smaller than 0.5, moderately stable if the ratio is 0.6--0.8, and unstable if the ratio exceeds 0.8.

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