Abstract: In nonregular smooth function models with vanishing first derivative, the conventional bootstrap is known to be inconsistent, whereas theout 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.