Essays on Inference in Non-standard Situations

Abstract

This dissertation consists of three essays on inference in non-standard scenarios. The first essay investigates inference on union bounds, prevalent in various empirical contexts such as relaxations of the difference-in-differences assumption and counterfactual analysis with partially identified structural parameters. I propose novel methods for both finite and infinite sets of bounds.The second essay presents a bootstrap-based profiling inference technique for subvectors in moment inequality models. By refining critical value calculation and simplifying non-linear moment conditions, this method offers improved computational efficiency upon existing methods.The third essay, conducted jointly with Dante Amengual and Enrique Sentana, extends score-type tests in likelihood contexts with a null information matrix greater than one. Our approach, leveraging higher-order derivatives, is asymptotically equivalent to likelihood ratio tests while requiring estimation only under the null.