Abstract: Looking myopically at the larger features of the likelihood function, absent some fine detail, can theoretically improve maximum likelihood estimation. Such estimators are, in fact, used routinely, since numerical techniques for maximizing a computationally expensive likelihood function or for maximizing a Monte Carlo approximation to a likelihood function may be unable to investigate small scale behavior of the likelihood. A class of maximum smoothed likelihood estimators is introduced and shown to be asymptotically efficient for models possessing local asymptotic normality. This theoretical result corresponds to good finite sample properties in two examples, with a likelihood that is smooth but multimodal, and a likelihood that is not smooth.
Key words and phrases: Likelihood, local asymptotic normality, maximum likelihood estimation, maximum smoothed likelihood estimation, smoothing.