Abstract: In nonregular smooth function models with vanishing first derivative, the conventional bootstrap is known to be inconsistent, whereas the out of bootstrap is consistent. We explore the effects of iterating the out of bootstrap on coverage accuracy of bootstrap percentile confidence intervals in such models, and develop a special iterative scheme which outperforms the non-iterated out of bootstrap in terms of asymptotic coverage accuracy. Several numerical examples are presented to motivate our development and illustrate its theoretical findings.
Key words and phrases: bootstrap iteration, m out of n bootstrap, smooth function model.