Assessing parameter uncertainty via bootstrap likelihood ratio confidence regions

In this paper, we show that, under certain regularity conditions, constructing likelihood ratio confidence regions using a boostrap estimate of the distribution of the likelihood ratio statistic-instead of the usual chi 2 approximation-leads to regions which have a coverage error of O(n- 2), which is the same as that achieved using a Bartlett-corrected likelihood ratio statistic. We use the boostrap method to assess the uncertainty associated with dose-response parameters that arise in models for the Japanese atomic bomb survivors data.