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Median Regularity and Honest Inference
Arun Kumar Kuchibhotla, Sivaraman Balakrishnan, Larry Wasserman · 2022-06-07 · via math.ST updates on arXiv.org

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.

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