Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 47 / 4 / b / ii / Solution

For each bootstrap replicate form the studentized pivotLet $t_{.025}^{\ast },t_{.975}^{\ast }$ be its empirical quantiles. The bootstrap-t confidence interval approximatesSolving both inequalities for $\theta$ reverses the quantile order, givingUsing the same fixed standard error in every bootstrap numerator would not implement this studentized procedure; each replicate needs its own ${\hat{s}}^{\ast }$.