 
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,
PoNing Chen, Senior Member, IEEE, and
Ziad Rached, Student Member, IEEE
AbstractIn [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
