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B1092
Topic: Title: Partial identification in linear models: Regression with interval-valued data Authors:  Georg Schollmeyer - Ludwig Maximilaians University Munich (Germany) [presenting]
Thomas Augustin - LMU Munich (Germany)
Abstract: In many situations of statistical analysis, the variables of actual interest cannot be observed in the precision that is needed to meet the requirements to justify the application a classical standard procedure of statistical data analysis. One prominent example is the request of the income of participants in a survey. There, respondents often refute an answer and one has to deal with a big amount of missing values that could not be treated as missing at random. One way to circumvent this problem is to allow respondents to give a categorized answer about their income to decreases non-response. In this situation, parametric statistical models are generally only partially identified, meaning that also with an infinite amount of data, there is still a rest of systematic uncertainty about the true parameter(s) because different parameter settings could lead to exactly the same distribution of the observed coarsed income. Instead of imposing further, often unjustified assumptions to enforce model identification, the methodology of partial identification deals with the identification problem by looking at the set of parameter settings compatible with the observable random variables and the underlying assumed model. We compare approaches for estimating partially identified linear models based on moment inequalities with other approaches that essentially determine the envelopes of estimates arising from all potential data completions.