On nonparametric estimation of a mixing density via the predictive recursion algorithm

Understand

Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem.

• This paper surveys the literature on a fast, recursive estimator based on the predictive recursion algorithm.
• After introducing the algorithm and giving a few examples, I summarize the available asymptotic convergence theory, describe an important semiparametric extension, and highlight two interesting applications.
• I conclude with a discussion of several recent developments in this area and some open problems.