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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: 388
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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