Abstract
This paper is concerned with parametric estimation in a situation where the parameter space is restricted. The maximum likelihood solution often occurs outside the parameter space, which is termed as the improper solution. We take a unified approach to the problem in terms of using a prior density which vanishes outside the parameter space. The modified estimate is defined by minimization of the posterior density. The solution is guaranteed to exist almost surely in the parameter space. The method extends directly to other methods of estimation, the so-called minimum contrast methods. The influence of the modification in asymptotic content is investigated.
