On the Uniqueness of the Maximum Likelihood Estimator

Abstract Orme [Econ. Rev. 8 (1989) 217] attempted to demonstrate that any solution to the likelihood equations for the truncated normal regression will be unique and will also be the global maximiser of the log-likelihood function. The argument rested on showing local concavity at any stationary point. Although sufficient in the scalar parameter case, this condition does not guarantee uniqueness of an interior local maximum in the multidimensional case. The present note addresses this issue.