A general upper bound of likelihood ratio for regression
This paper discusses the likelihood ratio test statistics (LRTS) in regression problems, and derives a general upper bound of the asymptotic order of LRTS for the sample size n. In some cases of estimation, where the true parameter is not identifiable, the LRTS diverges to infinity asymptotically. It is also known that the LRTS of some nonlinear models has a lower bound of the order logn. This paper shows logn gives an upper bound of the asymptotic order of regression under very general assumptions, which are satisfied by many practical probability models including the Gaussian noise and the binary regression.