No . 858 November 07 , 2002 A general upper bound of likelihood ratio in binary regression
We derive a general upper bound of the asymptotic order of the likelihood ratio test statistics (LRTS) for binary regression. It has been known that in some unidentifiable cases of nonlinear regression the LRTS may diverge to infinity asymptotically and have a log n lower bound for the sample size n. This paper shows an upper bound of log n under the very general assumptions of the finiteness of VC dimension of the regressor class and the boundedness of the assumed true regressor.