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Topic: ? false-positive and false-negative
Replies: 4   Last Post: Sep 16, 2011 3:37 PM

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Herman Rubin

Posts: 335
Registered: 2/4/10
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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