This paper considers uniformly valid (over a class of data generating processes) inference for convex functionals of partially identified parameters in cases where the identified set is defined by convex (in the parameter) moment inequalities. We propose a bootstrap procedure for constructing uniformly valid confidence sets for a convex functional of a partially identified parameter. The proposed method amounts to bootstrapping the value functions of a convex optimization problem, and subsumes subvector inference as a special case.  Unlike other proposed subvector inference procedures, our procedure does not require the researcher to repeatedly invert a hypothesis test, and is extremely computationally efficient . Finally, we discuss sufficient conditions on the moment functions to ensure uniform validity, and show that our assumptions are in fact satisfied by a large class of data generating processes .
This paper considers uniformly valid (over a class of data generating processes) inference for linear functionals of partially identified parameters in cases where the identified set is defined by linear (in the parameter) moment inequalities. We propose a bootstrap procedure for constructing uniformly valid confidence sets for a linear functional of a partially identified parameter. The proposed method amounts to bootstrapping the value functions of a linear optimization problem, and subsumes subvector inference as a special case. In other words, this paper shows the conditions under which naively bootstrapping a linear program can be used to construct a confidence set with uniform correct coverage for a partially identified linear functional. Unlike other proposed subvector inference procedures, our procedure does not require the researcher to repeatedly invert a hypothesis test, and is extremely computationally efficient .
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convex
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convex
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In other words, this paper shows the conditions under which naively bootstrapping a linear program can be used to construct a confidence set with uniform correct coverage for a partially identified linear functional.
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. Finally, we discuss sufficient conditions on the moment functions to ensure uniform validity, and show that our assumptions are in fact satisfied by a large class of data generating processes