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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 50, NO. 4, APRIL 2004 663 Csiszr's Cutoff Rates for the General
 

Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 50, NO. 4, APRIL 2004 663
Csiszár's Cutoff Rates for the General
Hypothesis Testing Problem
Fady Alajaji, Senior Member, IEEE,
Po-Ning Chen, Senior Member, IEEE, and
Ziad Rached, Student Member, IEEE
Abstract--In [6], Csiszár established the concept of forward -cutoff
rate for the error exponent hypothesis testing problem based on indepen-
dent and identically distributed (i.i.d.) observations. Given 0, he
defined the forward -cutoff rate as the number 0 that provides
the best possible lower bound in the form ( ) to the type 1
error exponent function for hypothesis testing where 0
is the rate of exponential convergence to 0 of the type 2 error proba-
bility. He then demonstrated that the forward -cutoff rate is given by
( ), where ( ) denotes the Rényi -divergence
[19], 0, = 1. Similarly, for 0 1, Csiszár also established
the concept of reverse -cutoff rate for the correct exponent hypothesis
testing problem.
In this work, we extend Csiszár's results by investigating the forward
and reverse -cutoff rates for the hypothesis testing between two arbi-

  

Source: Alajaji, Fady - Department of Mathematics and Statistics, Queen's University (Kingston)

 

Collections: Engineering