DocumentCode :
930581
Title :
Distribution-free performance bounds for potential function rules
Author :
Devroye, Luc P. ; Wagner, T.J.
Volume :
25
Issue :
5
fYear :
1979
fDate :
9/1/1979 12:00:00 AM
Firstpage :
601
Lastpage :
604
Abstract :
In the discrimination problem the random variable 
, known to take values in 
, is estimated from the random vector 
. All that is known about the joint distribution of 
is that which can be inferred from a sample 
of size 
drawn from that distribution. A discrimination nde is any procedure which determines a decision 
for from and 
. For rules which are determined by potential functions it is shown that the mean-square difference between the probability of error for the nde and its deleted estimate is bounded by 
where 
is an explicitly given constant depending only on 
and the potential function. The 
behavior is shown to be the best possible for one of the most commonly encountered rules of this type.
, known to take values in , is estimated from the random vector . All that is known about the joint distribution of is that which can be inferred from a sample of size drawn from that distribution. A discrimination nde is any procedure which determines a decision for from and . For rules which are determined by potential functions it is shown that the mean-square difference between the probability of error for the nde and its deleted estimate is bounded by where is an explicitly given constant depending only on and the potential function. The behavior is shown to be the best possible for one of the most commonly encountered rules of this type.Keywords :
Nonparametric estimation; Pattern classification; Computer errors; Computer science; Histograms; Kernel; Nearest neighbor searches; Random variables; State estimation; US Department of Defense; Upper bound; Voting;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1979.1056087
Filename :
1056087
Link To Document :
