The Likelihood Pivot: Performing Inference with Confidence
Advisor: Peter Hoff Maximum likelihood estimation is a popular method of statistical inference in part due to its efficiency. Unfortunately, much of the efficiency is lost when the model has been misspecified. To account for possible model misspecification, the sandwich estimate of variance can be used with MLE inference to generate asymptotically correct confidence intervals, but these intervals typically perform poorly at small sample sizes. In this talk, we present a pivot-based method that performs better than the sandwich and its adjustments at small sample sizes. Further, an asymptotic efficiency result is described which shows that the pivot-based confidence intervals perform as well as sandwich-based confidence intervals for large sample sizes. We also explore this pivot in a Bayesian setting. Previous research has shown that pivots cannot be used in a proper Bayesian analysis, but we present a framework for using pivots in a pseudo-Bayesian analysis. Finally, we use a real world dataset as our population and show that our pivot performs favorably against the sandwich, in terms of coverage of the true parameter.