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\noindent Statistica Sinica {\bf 15}(2005), 945-967

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\centerline{\large\bf ITERATING THE {\bf m} OUT OF {\bf n} BOOTSTRAP}
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\centerline{\large\bf IN NONREGULAR SMOOTH FUNCTION MODELS}
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\author{K. Y. Cheung$^1$, Stephen M. S. Lee$^1$ and G. Alastair Young$^2$}
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\centerline{\it $^1$The University of Hong Kong and $^2$Imperial College London}
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\begin{quotation}
\noindent {\it 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.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
bootstrap iteration, $m$ out of $n$ bootstrap, smooth function model.\par
\end{quotation}

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