Variance stabilization and the bootstrap

We investigate the use of a variance stabilizing transformation for the computation of a bootstrap t confidence interval. The transformation is estimated in an ‘automatic’ manner through an initial bootstrap step. A bootstrap t interval is then computed for the variance stabilized parameter and the interval is mapped back to the original scale. The resultant procedure is second-order correct in some settings, invariant and in a number of examples it performs better than the usual untransformed bootstrap / interval. It also requires far less computation. The new interval is compared with Efron's BCa procedure and the two methods are seen to produce similar results.