Importance of interpolation when constructing double-bootstrap confidence intervals

We show that, in the context of double-bootstrap confidence intervals, line ar interpolation at the second level of the double bootstrap can reduce the simulation error component of coverage error by an order of magnitude. Int ervals that are indistinguishable in terms of coverage error with theoretic al, infinite simulation, double-bootstrap confidence intervals may be obtai ned at substantially less computational expense than by using the standard Monte Carlo approximation method. The intervals retain the simplicity of un iform bootstrap sampling and require no special analysis or computational t echniques. Interpolation at the first level of the double bootstrap is show n to have a relatively minor effect on the simulation error.