Robust tests for the common principal components model

RODRIGUES, ISABEL; BOENTE, GRACIELA; PIRES, ANA M.

Jyväskylä, Finlandia

Congreso; International Conference on Robust Statistics (ICORS 2005); 2005

In multivariate analysis we often deal with situations involving several populations, such as discriminant analysis, where the assumption of equality of scatter matrices is usually assumed. Yet sometimes, this assumption is not adequate but problems related to an excessive number of parameters will arise if we estimate the scatter matrices separately for each population. In many practical situations this problem can be avoided if the scatter matrices of the different populations exhibit some common structure. In Flury (1988) a unified study of the maximum likelihood estimators under a CPC  model and under a proportionality model is given and likelihood ratio tests for a hierarchy of models is studied. However, as it is well known, the likelihood ratio test are in most situations affected by anomalous observations. In this work we propose robust procedures for testing the relationship between scatter matrices. An robust statistic for testing proportionality against a common principal components model is considered. Also, the null hypothesis of a CPC model versus no restrictions on the scatter matrices is studied. In Flury (1988) a unified study of the maximum likelihood estimators under a CPC  model and under a proportionality model is given and likelihood ratio tests for a hierarchy of models is studied. However, as it is well known, the likelihood ratio test are in most situations affected by anomalous observations. In this work we propose robust procedures for testing the relationship between scatter matrices. An robust statistic for testing proportionality against a common principal components model is considered. Also, the null hypothesis of a CPC model versus no restrictions on the scatter matrices is studied.