Efficient Construction of Test-Inversion Confidence Intervals Using Quantile Regression, With Application To Population Genetics

TL;DR

This paper introduces a fast, efficient method for constructing bootstrap confidence intervals using quantile regression, significantly reducing computational effort in complex statistical inference problems, exemplified by population genetics applications.

Contribution

It develops a novel quantile regression-based approach for rapid test-inversion bootstrap confidence intervals, improving efficiency over existing stochastic approximation methods.

Findings

Achieves up to 40% reduction in simulations needed

Demonstrates effectiveness on Watterson estimator in population genetics

Provides a practical alternative for complex estimators with difficult distributions

Abstract

Modern problems in statistics tend to include estimators of high computational complexity and with complicated distributions. Statistical inference on such estimators usually relies on asymptotic normality assumptions, however, such assumptions are often not applicable for available sample sizes, due to dependencies in the data and other causes. A common alternative is the use of re-sampling procedures, such as the bootstrap, but these may be computationally intensive to an extent that renders them impractical for modern problems. In this paper we develop a method for fast construction of test-inversion bootstrap confidence intervals. Our approach uses quantile regression to model the quantile of an estimator conditional on the true value of the parameter, and we apply it on the Watterson estimator of mutation rate in a standard coalescent model. We demonstrate an improved efficiency of up to 40% from using quantile regression compared to state of the art methods based on stochastic approximation, as measured by the number of simulations required to achieve comparable accuracy.