Abstract:  We consider a semiparametric mixture of two density functions where one of them is known while the weight and the other function are unknown. We do not assume any additional structure on the unknown density function.  We suggest a novel approach to estimation of this model that is based on an idea of applying a maximum smoothed likelihood to what would otherwise have been an ill-posed problem. We introduce an iterative MM (Majorization-Minimization) algorithm that estimates all of the model parameters. Unlike possible competing methods, this algorithm works well in both univariate as well as multivariate case. We establish that the algorithm possesses a descent property with respect to a log-likelihood objective functional and prove that the algorithm, indeed, converges. Finally, we also illustrate the performance of our algorithm in a simulation study and using a real dataset.