Median Regularity and Honest Inference

06/07/2022

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by   Arun Kumar Kuchibhotla, et al.

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We introduce a new notion of regularity of an estimator called median regularity. We prove that uniformly valid (honest) inference for a functional is possible if and only if there exists a median regular estimator of that functional. To our knowledge, such a notion of regularity that is necessary for uniformly valid inference is unavailable in the literature.