EXISTENCE AND CONSISTENCY OF A NONPARAMETRIC ESTIMATOR OF PROBABILITY MEASURES IN THE PROHOROV METRIC FRAMEWORK
Harvey Thomas Banks, W. Clayton Thompson · International Journal of Pure and Apllied Mathematics · 2015
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 [3,6,15,18,20].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. Motivation and Problem FormulationIn a standard nonlinear regression problem, a mathematical model is proposed which links one or more states of interest to the independent variables (regressors) of an experiment and to a vector of parameters whose values are