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Many criteria and procedures to select a reasonable subset of variables in the context of principal component analysis have been derived, but there still exist problems to determine how many variables should be selected as well as to evaluate the performance of the selection methods. To deal with these problems, two computer intensive methods are performed: a bootstrap method which is applied to the given subsets of variables and a cross validation method which is modified for principal component analysis. The results in some numerical examples offer information and some guidance to determine the number of variables to be selected.
