Principal Components of sample estimates: an approach through Symbolic Data Analysis

This paper deals with the analysis of datasets, where the subjects are
described by the estimated means of a p-dimensional variable. Classical statistical
methods of data analysis do not treat measurements affected by intrinsic
variability, as in the case of estimates, so that the heterogeneity induced among
subjects by this condition is not taken into account. In this paper a way to solve
the problem is suggested in the context of symbolic data analysis, whose specific
aim is to handle data tables where single valued measurements are substituted
by complex data structures like frequency distributions, intervals, and sets of
values. A principal component analysis is carried out according to this proposal,
with a significant improvement in the treatment of information.