Least squares estimation of a k-monotone density function

The fact that a k-monotone density can be defined by means of a mixing distribution makes its estimation feasible within the framework of mixture models. It turns the problem naturally into estimating a mixing distribution, nonparametrically. This paper studies the least squares approach to solving this problem and presents two algorithms for computing the estimate. The resulting mixture density is hence just the least squares estimate of the k-monotone density. Through simulated and real data examples, the usefulness of the least squares density estimator is demonstrated.