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R function which finds confidence interval for binomial variance

4 messages · Robert A. LaBudde, Ralph Scherer, Robert A LaBudde +1 more

#
I need to construct confidence intervals for the binomial variance. 
This is the usual estimate

	v = x*(n-x)/n

or its unbiased counterpart

	v' = x*(n-x)/(n-1)

where x = binomial number of successes observed in n Bernoulli trials 
from proportion p.

The usual X^2 method for variance confidence intervals will not work, 
because of the strong non-normal character of the sampling 
distribution for v (or v').

Does anyone know of an R package with R function that computes a 
reasonable confidence interval for v or v'?

Thanks.
================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"
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Hello Robert,

would it be an idea to construct CI's with bootstrap methods?
If yes, you can use package "boot", based on the book of Davison & Hinkley or 
the package "bootstrap", based on the book of Efron &Tibshirani.
You can put the estimator inside for argument "theta".

Bests,
Ralph

Am Thursday 25 September 2008 07:56:56 schrieb Robert A. LaBudde:
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Thanks Ralph, Moshe and ctu at bigred.unl.edu for you helpful comments.

Using bootstrap (e.g., 'boot' + boot.ci()) for the confidence 
interval on the variance is not very accurate in coverage, because 
the sampling distribution is extremely skewed. In fact, the 'BCa' 
method returns the same result as the Efron 'percent' method.

Moshe's idea of treating the confidence interval for the binomial 
variance as a transform of the confidence interval for the binomial 
proportion is elegant (Doh! Why didn't I think of that?), except that 
the transform is bivalued, although monotonic on each branch, with 
the branch point singularity at p=0.5.

The bootstrap method does not have much coverage accuracy for any 
proportion, for n=6, 12 and 20, and the proportion method works great 
for n=6, 12, 20 and 50, except near p = 0.5, where it fails to 
achieve reasonable coverage.

So I'm still looking for a reliable method for all p and for reasonable n.

The proportion-based method is the best I've found, so far.
================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"