Statistica Sinica 15(2005), 945-967

ITERATING THE m OUT OF n BOOTSTRAP

IN NONREGULAR SMOOTH FUNCTION MODELS

K. Y. Cheung$^1$, Stephen M. S. Lee$^1$ and G. Alastair Young$^2$

$^1$The University of Hong Kong and $^2$Imperial College London

Abstract: In nonregular smooth function models with vanishing first derivative, the conventional bootstrap is known to be inconsistent, whereas the $m$ out of $n$ bootstrap is consistent. We explore the effects of iterating the $m$ out of $n$ bootstrap on coverage accuracy of bootstrap percentile confidence intervals in such models, and develop a special iterative scheme which outperforms the non-iterated $m$ out of $n$ 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.