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Conference Paper: Iterating the m out of n bootstrap for smooth function models with null derivatives
Title  Iterating the m out of n bootstrap for smooth function models with null derivatives 

Authors  
Issue Date  2004 
Citation  The 6th World Congress of the Bernoulli Society for Mathematical Statistics and Probability and the 67th Annual Meeting of the Institute of Mathematical Statistics, Barcelona, Spain, 2631 July 2004, Abstract no. 235 How to Cite? 
Abstract  The bootstrap provides an attractive approach to nonparametric
inference on a scalar parameter θ of interest. In certain situations
validity of the conventional n out of n bootstrap may depend
on the true value of the parameter. The m out of n bootstrap
is well known to produce consistent estimators of sampling distributions
in nonregular problems, where the conventional bootstrap
breaks down, but is often accompanied by a loss in efficiency as compared to regular applications of the conventional
bootstrap. Of theoretical and practical importance is the question
of whether iteration can improve the m out of n bootstrap
by reducing its asymptotic error.
The problem of constructing a confidence interval for a function
θ of a population mean under regularity conditions, but with the
function having a null derivative at the true population mean,
provides an important testing ground for analysis of iteration
of the m out of n bootstrap. In this setting substitution estimators
are nconsistent with limiting chisquared type distributions,
and the n out of n bootstrap is inconsistent for their sampling
distributions. The m out of n bootstrap percentile method interval
is, by contrast, found to be consistent, incurring a onesided
coverage error of order O(n
−1/2
) if m is chosen optimally. We
propose a new scheme for iterating the m out of n bootstrap to
reduce the coverage error further to order O(n
−2/3
), provided
that the firstlevel and secondlevel bootstrap resample sizes are
appropriately chosen. Our new scheme is computationally directly
comparable to the conventional bootstrap iterative scheme
as would have been used in regular settings.
Several numerical examples, including a natural application of
bootstrap confidence intervals in a hypothesis testing problem,
are presented to motivate our development and illustrate the theoretical
findings. 
Persistent Identifier  http://hdl.handle.net/10722/110208 
DC Field  Value  Language 

dc.contributor.author  Cheung, KY  en_HK 
dc.contributor.author  Lee, SMS  en_HK 
dc.date.accessioned  20100926T01:55:53Z   
dc.date.available  20100926T01:55:53Z   
dc.date.issued  2004  en_HK 
dc.identifier.citation  The 6th World Congress of the Bernoulli Society for Mathematical Statistics and Probability and the 67th Annual Meeting of the Institute of Mathematical Statistics, Barcelona, Spain, 2631 July 2004, Abstract no. 235   
dc.identifier.uri  http://hdl.handle.net/10722/110208   
dc.description.abstract  The bootstrap provides an attractive approach to nonparametric inference on a scalar parameter θ of interest. In certain situations validity of the conventional n out of n bootstrap may depend on the true value of the parameter. The m out of n bootstrap is well known to produce consistent estimators of sampling distributions in nonregular problems, where the conventional bootstrap breaks down, but is often accompanied by a loss in efficiency as compared to regular applications of the conventional bootstrap. Of theoretical and practical importance is the question of whether iteration can improve the m out of n bootstrap by reducing its asymptotic error. The problem of constructing a confidence interval for a function θ of a population mean under regularity conditions, but with the function having a null derivative at the true population mean, provides an important testing ground for analysis of iteration of the m out of n bootstrap. In this setting substitution estimators are nconsistent with limiting chisquared type distributions, and the n out of n bootstrap is inconsistent for their sampling distributions. The m out of n bootstrap percentile method interval is, by contrast, found to be consistent, incurring a onesided coverage error of order O(n −1/2 ) if m is chosen optimally. We propose a new scheme for iterating the m out of n bootstrap to reduce the coverage error further to order O(n −2/3 ), provided that the firstlevel and secondlevel bootstrap resample sizes are appropriately chosen. Our new scheme is computationally directly comparable to the conventional bootstrap iterative scheme as would have been used in regular settings. Several numerical examples, including a natural application of bootstrap confidence intervals in a hypothesis testing problem, are presented to motivate our development and illustrate the theoretical findings.   
dc.language  eng  en_HK 
dc.relation.ispartof  The 6th World Congress of the Bernoulli Society for Mathematical Statistics and Probability and the 67th Annual Meeting of the Institute of Mathematical Statistics  en_HK 
dc.title  Iterating the m out of n bootstrap for smooth function models with null derivatives  en_HK 
dc.type  Conference_Paper  en_HK 
dc.identifier.email  Lee, SMS: smslee@hkusua.hku.hk  en_HK 
dc.identifier.authority  Lee, SMS=rp00726  en_HK 
dc.identifier.hkuros  115394  en_HK 