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: We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades. Significant new theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other) least squares estimates for the measure estimation problem.

Least Squares Estimation of Probability Measures in the Prohorov Metric Framework