
Re: ? falsepositive and falsenegative
Posted:
Sep 16, 2011 2:38 PM


On 20110916, Cosine <asecant@gmail.com> wrote: > Hi:
> Is it possible to simultaneously reduce the rate of falsepositive > and the rate > of falsenegative?
> 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)4946054 FAX: (765)4940558

