Adaptive robust confidence intervals
Abstract
This paper studies the construction of adaptive confidence intervals under Huber’s contamination model when the contamination proportion is unknown. For the robust confidence interval of a Gaussian mean, we show that the optimal length of an adaptive interval must be exponentially wider than that of a nonadaptive one. An optimal construction is achieved through simultaneous uncertainty quantification of quantiles at all levels. The results are further extended beyond the Gaussian location model by addressing a general family of robust hypothesis testing. In contrast to adaptive robust estimation, our findings reveal that the optimal length of an adaptive robust confidence interval critically depends on the distribution’s shape.
Fields of Study & Subjects
Fault Detection and Control Systems
Control Systems and Identification
Statistical Methods and Inference
Publication details
- Journal / source
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Volume
- 54
- Issue
- 3
- Pages
- 1128-1152
- Publication date
- 1 June 2026
- Language
- EN