A numerical method to obtain exact confidence intervals for likelihood-based parameter estimators

Abstract

We propose a numerical method for obtaining exact confidence intervals of likelihood-based parameter estimators for general multi-parameter models. Although the test inversion method provides exact confidence intervals, it is applicable only to single-parameter models. Our new method can be applied to general multi-parameter models without loss of accuracy, which is in sharp contrast to other multi-parameter extensions of the test inversion. Using Monte Carlo simulations, we show that our method is feasible and provides correct coverage probabilities in finite samples.