A Pivot-Based Improvement to Sandwich-Based Confidence Intervals

TL;DR

This paper introduces a pivot-based method for constructing confidence intervals that improves small-sample coverage accuracy over traditional sandwich-based intervals, especially under model misspecification.

Contribution

It develops a novel pivot-based approach that eliminates the plug-in assumption, enhancing small-sample coverage while maintaining asymptotic efficiency.

Findings

Pivot-based intervals outperform sandwich intervals in small samples.

The method achieves asymptotic efficiency comparable to sandwich intervals.

Simulation studies confirm improved coverage accuracy.

Abstract

The current standard for confidence interval construction in the context of a possibly misspecified model is to use an interval based on the sandwich estimate of variance. These intervals provide asymptotically correct coverage, but small-sample coverage is known to be poor. By eliminating a plug-in assumption, we derive a pivot-based method for confidence interval construction under possibly misspecified models. When compared against confidence intervals generated by the sandwich estimate of variance, this method provides more accurate coverage of the pseudo-true parameter at small sample sizes. This is shown in the results of several simulation studies. Asymptotic results show that our pivot-based intervals have large sample efficiency equal to that of intervals based on the sandwich estimate of variance.