Rank Conditional Coverage and Confidence Intervals in High-Dimensional Problems.

Area of Science:

• Statistics
• High-Dimensional Data Analysis
• Statistical Inference

Background:

• Traditional confidence intervals fail in high-dimensional settings, leading to low coverage for significant estimates.
• Existing selection adjustment methods control coverage within selected sets but may not address rank-based coverage issues.
• The relationship between estimate significance rank and interval coverage is critical for reliable inference.

Purpose of the Study:

• To propose rank conditional coverage (RCC) as a novel criterion for confidence intervals in high-dimensional multiple testing/covering problems.
• To develop and evaluate bootstrapping methods for constructing confidence intervals that control RCC.
• To improve the accuracy and reduce the size of confidence intervals in high-dimensional inference.

Main Methods:

• Introduced rank conditional coverage (RCC) as the expected coverage rate conditional on the significance rank of an estimator.
• Developed two bootstrapping-based methods to construct confidence intervals that control the proposed RCC criterion.
• Evaluated the performance of RCC-controlling intervals against marginal and selection adjusted intervals.

Main Results:

• Marginal and selection adjusted confidence intervals exhibit low coverage for highly significant estimates.
• The proposed RCC criterion addresses the coverage gap for significant parameters.
• Bootstrapping methods controlling RCC yield smaller intervals with improved coverage, especially for top-ranked estimates.

Conclusions:

• Rank conditional coverage (RCC) offers a more appropriate criterion for confidence intervals in high-dimensional settings.
• The developed bootstrapping methods provide a practical solution for constructing reliable confidence intervals.
• These methods enhance statistical inference by ensuring better coverage for the most significant findings.