Show simple item record Beresteanu, Arie en_US Molinari, Francesca en_US 2010-03-09T15:26:48Z 2010-03-09T15:26:48Z 2008 en_US
dc.description.abstract We propose inference procedures for partially identified population features for which the population identification region can be written as a transformation of the Aumann expectation of a properly defined set valued random variable (SVRV). An SVRV is a mapping that associates a set (rather than a real number) with each element of the sample space. Examples of population features in this class include sample means and best linear predictors with interval outcome data, and parameters of semiparametric binary models with interval regressor data. We extend the analogy principle to SVRVs, and show that the sample analog estimator of the population identification region is given by a transformation of a Minkowski average of SVRVs. Using the results of the mathematics literature on SVRVs, we show that this estimator converges in probability to the identification region of the model with respect to the Hausdorff distance. We then show that the Hausdorff distance between the estimator and the population identification region, when properly normalized by ?n, converges in distribution to the supremum of a Gaussian process whose covariance kernel depends on parameters of the population identification region. We provide consistent bootstrap procedures to approximate this limiting distribution. Using similar arguments as those applied for vector valued random variables, we develop a methodology to test assumptions about the true identification region and to calculate the power of the test. We show that these results can be used to construct a confidence collection, that is a collection of sets that, when specified as null hypothesis for the true value of the population identification region, cannot be rejected by our test. en_US
dc.format.extent 408540 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.publisher Econometrica en_US
dc.subject Partial identification en_US
dc.subject confidence collections en_US
dc.subject set valued random variables en_US
dc.title Asymptotic Properties for a Class of Partially Identified Models en_US
dc.type Journal Article en_US
dc.department Economics

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