
Dear Professor Lumley;
 
Thank you so much for your invaluable advice!
 
I will digest your advice and try different methods.
 
Great thanks again!
 
Faye 
 
> Date: Fri, 5 Nov 2010 08:24:00 +1300
> Subject: Re: [R] How to do bootstrap for the complex sample design?
> From: tlumley@uw.edu
> To: TimHesterberg@gmail.com
> CC: feixu78@hotmail.com; r-help@r-project.org
> 
> On Fri, Nov 5, 2010 at 3:51 AM, Tim Hesterberg <timhesterberg@gmail.com> wrote:
> > Faye wrote:
> >>Our survey is structured as : To be investigated area is divided into
> >>6 regions, within each region, one urban community and one rural
> >>community are randomly selected, then samples are randomly drawn from
> >>each selected uran and rural community.
> >>
> >>The problems is that in urban/rural stratum, we only have one sample.
> >>In this case, how to do bootstrap?
> >
> > You are lucky that your sample size is 1.  If it were 2 you would
> > probably have proceeded without realizing that the answers were wrong.
> >
> > Suppose you had two samples in each stratum.  If you proceed naturally,
> > drawing bootstrap samples of size 2 from each stratum, this would
> > underestimate variability by a factor of 2.
> >
> > In general the ordinary nonparametric bootstrap estimates of variability
> > are biased downward by a factor of (n-1)/n -- exactly for the mean,
> > approximately for other statistics.  In multiple-sample and stratified
> > situations, the bias depends on the stratum sizes.
> >
> > Three remedies are:
> > * draw bootstrap samples of size n-1
> > * "bootknife" sampling - omit one observation (a jackknife sample), then
> >  draw a bootstrap sample of size n from that
> > * bootstrap from a kernel density estimate, with kernel covariance equal
> >  to empirical covariance (with divisor n-1) / n.
> > The latter two are described in
> > Hesterberg, Tim C. (2004), Unbiasing the Bootstrap-Bootknife Sampling vs. Smoothing, Proceedings of the Section on Statistics and the Environment, American Statistical Association, 2924-2930.
> > http://home.comcast.net/~timhesterberg/articles/JSM04-bootknife.pdf
> >
> > All three are undefined for samples of size 1.  You need to go to some
> > other bootstrap, e.g. a parametric bootstrap with variability estimated
> > from other data.
> >
> 
> And the 'survey' package supplies the first option. (It also supplies
> a bootstrap sample of size n that allows finite population
> corrections, designed for situations with a large n and a high
> sampling fraction, such as some business surveys.)
> 
> With a sample size of 1 per stratum there are no design-unbiased
> estimators of the standard error, so as others have said you need
> external data.
> 
> -thomas
> 
> 
> -- 
> Thomas Lumley
> Professor of Biostatistics
> University of Auckland
 		 	   		  
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