A Recursive Algorithm for Mixture of Densities Estimation

Recursive algorithms for the estimation of mixtures of densities have attracted a lot of attention in the last 10 years. Here an algorithm for recursive estimation is studied. It complements existing approaches in the literature, as it is based on conditions that are usually very weak. For example, the parameter space over which the mixture is taken does not need to be necessarily bounded. The essence of the procedure is to combine density estimation via empirical characteristic function together with an iterative Hilbert space approximation algorithm. The conditions for consistency of the estimator are verified for three important statistical problems. A simulation study is also included.