Traditional inference methods such as Wald and resampling methods require regular models and regular estimators. Unfortunately, many commonly considered models need not satisfy such regularity. Examples include OLS or MLE under increasing dimension, Monotone regression, Grenander estimator, estimators of mode, cube-root estimators. In this talk, I will present two general methods of inference that (at worst) only rely on the consistency (not on regularity) of the estimators for validity and if the estimator is rate-optimal, then the resulting confidence sets are rate adaptive as well. Applications to OLS and Manski's discrete choice model will be considered.
This is joint work with PhD students Kenta Takatsu and Woonyoung Chang available at https://arxiv.org/abs/2501.07772 and https://arxiv.org/abs/2407.12278.
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