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Modern problems in statistics tend to include estimators of highcomputational complexity and with complicated distributions. Statisticalinference on such estimators usually relies on asymptotic normalityassumptions, however, such assumptions are often not applicable for availablesample sizes, due to dependencies in the data and other causes. A commonalternative is the use of re-sampling procedures, such as the bootstrap, butthese may be computationally intensive to an extent that renders themimpractical for modern problems. In this paper we develop a method for fastconstruction of test-inversion bootstrap confidence intervals. Our approachuses quantile regression to model the quantile of an estimator conditional onthe true value of the parameter, and we apply it on the Watterson estimator ofmutation rate in a standard coalescent model. We demonstrate an improvedefficiency of up to 40% from using quantile regression compared to state of theart methods based on stochastic approximation, as measured by the number ofsimulations required to achieve comparable accuracy.

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