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Partial Identification in Regression Analysis
In many applied situations of regression analysis the variables one is actually interested in can not be directly observed or can not be observed in the resolution that is actually needed. This can for instance be due to a censoring or a coarsening of the data, or it can be due to measurement error, etc. In such situations, without further assumptions about the censoring- or coarsening process, or without additional knowledge about the measurement error, the obtained statistical model is usually only partially identified, which means that the underlying true regression parameters can not be estimated consistently. Therefore, within the methodology of partial identification, one does not try to estimate the true parameter, but instead one estimates so-called identification regions, which are subsets of the parameter space that contain all parameters that cannot be excluded with an infinite amount of observed data and the imposed model assumptions. In this talk, I would like to present certain identification regions in the context of (multiple) linear regression for the case where the outcome variable, the covariate(s), or both can only be observed in intervals. After discussing the case of interval-valued outcomes where different identification regions arise due to different imposed model assumptions, I would like to speak about the more difficult case where the covariates (and possibly also the outcomes) are interval-valued.
Georg Schollmeyer is a postdoctoral researcher in the working group 'Foundations of Statistics and Their Applications' headed by Thomas Augustin at the department of statistics at Ludwig-Maximilians-Universität (LMU) in munich. After studying mathematics at Technische Universität Dresden he went to munich to make a Phd in the field of imprecise probabilities. Under the supervision of Thomas Augustin he worked mostly on imprecise probabilities and partial identification in statistcs. Now, he is doing his habilitation at LMU, again under the supervision of Thomas Augustin.