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Re: st: implementation of variance formula


From   Robert A Yaffee <bob.yaffee@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: implementation of variance formula
Date   Thu, 12 Mar 2009 23:11:42 -0400

Inna,
   You should do about 10000 replications.  If I remember correctly,
that is what Efron suggested.  You could estimate the mean of the variance
or the variance itself, each time you resample.  I like the percentile method, 
myself.  It assumes an unbiased sample, but it will not work with small
samples.  If you know the distribution, you can do a bias correction.
    - Bob


Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University


Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2008.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: Inna Becher <inna.becher@uni-konstanz.de>
Date: Thursday, March 12, 2009 10:27 am
Subject: Re: st: implementation of variance formula
To: statalist@hsphsun2.harvard.edu


> Thank you, Robert. Are there two way of variance estimation: 1) 
> H-T-variance-estimation for each of 1000 replications and then mean of 
> 
> this variances as estimation of population variance and 2) H-T-mean 
> for 
> each replication and a bootstrap-estimation of  variance? Is there a 
> theoretical difference between these two ways?
> 
> Robert A Yaffee schrieb:
> > Inna,
> >   That could be an alternative to the H-T variance estimator.
> >          - Bob
> >
> > Robert A. Yaffee, Ph.D.
> > Research Professor
> > Silver School of Social Work
> > New York University
> >
> >
> > Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2008.pdf
> >
> > CV:  http://homepages.nyu.edu/~ray1/vita.pdf
> >
> > ----- Original Message -----
> > From: Inna Becher <inna.becher@uni-konstanz.de>
> > Date: Thursday, March 12, 2009 4:38 am
> > Subject: Re: st: implementation of variance formula
> > To: statalist@hsphsun2.harvard.edu
> >
> >
> >   
> >> Robert,
> >>
> >> I simulate 1000 samples from a population and for each sample I 
> >> calculate the H-T-estimator for the mean and I have to calculate 
> the 
> >> variance for the H-T-mean. Afterwards I'll investigate their 
> >> distribution over 1000 samples.
> >>
> >> Robert A Yaffee schrieb:
> >>     
> >>> Inna,
> >>>    Can you jacknife or bootstrap to obtain your variances?
> >>>          -   Bob
> >>>
> >>>
> >>> Robert A. Yaffee, Ph.D.
> >>> Research Professor
> >>> Silver School of Social Work
> >>> New York University
> >>>
> >>>
> >>> Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2008.pdf
> >>>
> >>> CV:  http://homepages.nyu.edu/~ray1/vita.pdf
> >>>
> >>> ----- Original Message -----
> >>> From: Inna Becher <inna.becher@uni-konstanz.de>
> >>> Date: Wednesday, March 11, 2009 4:50 am
> >>> Subject: Re: st: implementation of variance formula
> >>> To: statalist@hsphsun2.harvard.edu
> >>>
> >>>
> >>>   
> >>>       
> >>>> I can calculate the probability for each network (=cluster) to be 
> 
> >>>> included in the sample. I also can
> >>>> calculate for each pair of selected clusters to be included in 
> the 
> >>>>         
> >>>> sample. My problem is: this probabilities are to be saved 
> >>>>         
> >> somewhere. 
> >>     
> >>>> Should it be a matrix? I have not yet worked with matrices to 
> >>>> calculate 
> >>>> variances. The version of H-T-estimator I need is not implemented 
> 
> >>>>         
> >> in svy-.
> >>     
> >>>> I wrote an ado for sampling design that I need and implemented 
> >>>> H-T-estimator for the mean, but not for the variance.
> >>>>
> >>>> Steven Samuels schrieb:
> >>>>     
> >>>>         
> >>>>> Inna:
> >>>>>
> >>>>> You don't say which version of the H-T estimator you want; there 
> 
> >>>>>           
> >> are 
> >>     
> >>>>>       
> >>>>> many versions. The estimates themselves depend on knowing for 
> each 
> >>>>>           
> >>>>> cluster the probability that would be included in the sample. 
> This 
> >>>>>           
> >>>>> quantity must be supplied with the data set.  It might or might 
> 
> >>>>>           
> >> not 
> >>     
> >>>>>       
> >>>>>           
> >>>> be 
> >>>>     
> >>>>         
> >>>>> a simple function of the cluster "size" measure.
> >>>>>
> >>>>> Thel formulas for the variance of the classical H-T estimators 
> are 
> >>>>>           
> >>  
> >>     
> >>>>>       
> >>>>> also functions of the probability  that each pair of selected 
> >>>>>       
> >>>>>           
> >>>> clusters 
> >>>>     
> >>>>         
> >>>>> would be included in the sample; if there are m clusters in a 
> >>>>>       
> >>>>>           
> >>>> stratum, 
> >>>>     
> >>>>         
> >>>>> there  are m(m-1)/2  of these  probabilities.  Were they  
> supplied 
> >>>>>           
> >>>>> with the data set?  Even if  you have them, you would still have 
> 
> >>>>>           
> >> to 
> >>     
> >>>>>       
> >>>>> write your own (probably MATA) code  to utilize them.
> >>>>>
> >>>>> There is an alternative.  Stata's survey commands produce 
> modified 
> >>>>>           
> >>  
> >>     
> >>>>>       
> >>>>> H-T estimates .  You can obtain appropriate standard errors  if 
> 
> >>>>>           
> >> you  
> >>     
> >>>>>       
> >>>>> -syset- your data according to the design.
> >>>>>
> >>>>> On Mar 10, 2009, at 7:07 AM, Inna Becher wrote:
> >>>>>
> >>>>>       
> >>>>>           
> >>>>>> Dear statalisters,
> >>>>>>
> >>>>>> I have to implement a formula of the variance of modified 
> >>>>>> horvitz-thompson-estimator. My dataset is very large, so I 
> cannot 
> >>>>>>             
> >>>>>> produce a lot of new variables in order to do that. Should I 
> use 
> >>>>>>             
> >>>>>> mata? Are there any examples of implementing variance formulas 
> in 
> >>>>>>             
> >> stata?
> >>     
> >>>>>>         
> >>>>>>             
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