On 2011-09-16, Cosine <email@example.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?
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 firstname.lastname@example.org Phone: (765)494-6054 FAX: (765)494-0558