Cattaneo, Marco E. G. V.; Wiencierz, Andrea
(29. October 2011):
Robust regression with imprecise data.
Department of Statistics: Technical Reports, No.114

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Abstract
We consider the problem of regression analysis with imprecise data. By imprecise data we mean imprecise observations of precise quantities in the form of sets of values. In this paper, we explore a recently introduced likelihoodbased approach to regression with such data. The approach is very general, since it covers all kinds of imprecise data (i.e. not only intervals) and it is not restricted to linear regression. Its result consists of a set of functions, reflecting the entire uncertainty of the regression problem. Here we study in particular a robust special case of the likelihoodbased imprecise regression, which can be interpreted as a generalization of the method of least median of squares. Moreover, we apply it to data from a social survey, and compare it with other approaches to regression with imprecise data. It turns out that the likelihoodbased approach is the most generally applicable one and is the only approach accounting for multiple sources of uncertainty at the same time.