Robust generalized confidence intervals

ABSTRACT

Most interval estimates are derived from computable conditional distributions conditional on the data. In this article, we call the random variables having such conditional distributions confidence distribution variables and define their finite-sample breakdown values. Based on this, the definition of breakdown value of confidence intervals is introduced, which covers the breakdowns in both the coverage probability and interval length. High-breakdown confidence intervals are constructed by the structural method in location-scale families. Simulation results are presented to compare the traditional confidence intervals and their robust analogues.

KEYWORDS:

• Breakdown
• Confidence distribution
• Fiducial inference
• Generalized pivotal quantity
• Location-scale family
• Monte Carlo
• Simultaneous confidence intervals

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F25
• 62F35

Acknowledgments

This work was supported by Funding Project from BUCEA (Grant No. 21082716014, 00331616031), National Natural Science Foundation of China (Grant No. 11471172, 11601027, 11671386), Funding from Chinese Ministry of Science and Technology (Grant No. 2016YFF0203801), the National Center for Mathematics and Interdisciplinary Sciences, CAS, and Key Laboratory of Systems and Control, CAS. We thank the editor and referee for their constructive suggestions.