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Re: ? false-positive and false-negative
Posted:
Sep 16, 2011 2:38 PM
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On 2011-09-16, Cosine <asecant@gmail.com> wrote:
> Hi:
> Is it possible to simultaneously reduce the rate of false-positive
> and the rate
> of false-negative?
> Or this is intrincally impossible?
> Why?
> Thanks,
Assuming one has an admissible procedure, such as a unique
Bayes procedure or others, the answer is "no".
To see this, look at the classical problem of testing a
point null. If the acceptance region is enlarged, the
Type I error rate increases. If it is reduced, the Type
II error rate increases. If it is a "good" region,
exchanging acceptance and rejection parts will not help.
The problem in statistics is the optimal balancing of
risks. Good procedures are generally Bayes, but one
might have to accept approximations.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
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