Likelihood-based Imprecise Regression

Marco E. G. V. Cattaneo, Andrea Wiencierz

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We introduce a new approach to regression with imprecisely observed data, combining likelihood inference with ideas from imprecise probability theory, and thereby taking different kinds of uncertainty into account. The approach is very general: it provides a uniform theoretical framework for regression analysis with imprecise data, where all kinds of relationships between the variables of interest may be considered and all types of imprecisely observed data are allowed. Furthermore, we propose a regression method based on this approach, where no parametric distributional assumption is needed and likelihood-based interval estimates of quantiles of the residuals distribution are used to identify a set of plausible descriptions of the relationship of interest. Thus, the proposed regression method is very robust and yields a set-valued result, whose extent is determined by the amounts of both kinds of uncertainty involved in the regression problem with imprecise data: statistical uncertainty and indetermination. In addition, we apply our robust regression method to an interesting question in the social sciences by analyzing data from a social survey. As result we obtain a large set of plausible relationships, reflecting the high uncertainty inherent in the analyzed data set.

Original languageEnglish
Pages (from-to)1137-1154
Number of pages18
JournalInternational Journal of Approximate Reasoning
Issue number8
Early online date27 Jun 2012
Publication statusPublished - Nov 2012


  • Complex uncertainty
  • Imprecise data
  • Imprecise probability
  • Likelihood inference
  • Quantile estimation
  • Robust regression

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