Normal likelihoods and their relation to large sample theory of estimation

Normal likelihoods are shown to be associated with asymptotic normal distributions of large sample theory. An examination of the likelihood function can indicate when standard large sample theory of estimation can be applied and when it may be inaccurate and misleading to do so. Transformations that improve the accuracy and so extend the domain of application of asymptotic methods can sometimes be suggested by their effect on the likelihood function. An examination of the likelihood function can therefore prove useful in the usual application of the frequency theory approach to estimation.