Principal components of sample estimates: an approach through symbolic data analysis

This paper derives from a question arised during the analysis of an empirical dataset, where the subjects are described by the estimated means of a p-dimensional variable. Classical statistical methods of Data Analysis do not treat measurement 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 measurement are substituted by complex data structures like frequency distributions, intervals, sets of values. A Principal Component Analysis is carried out according to this proposal, with a significant improvement in the treatment of information.