Title: Adaptive Robust Confidence Intervals and Beyond
Abstract: In this talk, we study the construction of confidence intervals in statistical models with heterogeneous data, where an unknown fraction of observations deviates from a baseline structure. We consider three representative settings: Huber’s contamination model with unknown contamination proportion, Efron’s Gaussian two-groups model with unknown non-null proportion, and missing-not-at-random (MNAR) models with unknown missing rate.
Across these settings, we characterize the minimax-optimal lengths of confidence intervals that achieve valid coverage uniformly over the unknown nuisance parameters. Our results reveal a spectrum of adaptivity: in Huber’s model, adapting to an unknown contamination proportion incurs a severe loss in efficiency; in the two-groups model, the adaptation cost is milder but still unavoidable; in contrast, in MNAR models, no adaptation cost arises, and optimal rates can be achieved without knowledge of the missing rate.
These findings highlight a fundamental distinction between adaptive estimation and adaptive inference, and illustrate how the nature of heterogeneity—whether arising from contamination, latent structure, or missingness—governs the difficulty of uncertainty quantification.
3:30pm - Pre-talk meet and greet teatime - 219 Prospect Street, 13th floor, there will be light snacks and beverages in the kitchen area.
