Partitional Estimation Using Partial Moments

Abstract

Function approximation is at the heart of machine learning. Given a dataset comprised of inputs and outputs, we assume that there is an unknown underlying function that is consistent in mapping inputs to outputs in the target domain and resulted in the dataset. We then use supervised learning algorithms to approximate this function. We highlight the identical objective of multivariate nonparametric regressions, for both continuous and discrete outputs (dependent variables), using both numerical and categorical inputs (regressors). Underlying the multivariate nonparametric technique is the use of partitional based conditional estimation.

We examine 3 methods of partitioning and their resulting conditional estimates in evaluating unknown functional forms. We find the iterated means partitioning technique employed by the NNS R-package achieves superior mean-squared errors from the true forms in multivariate simulations.

Keywords: Partitional Estimation, kernels, nonparamteric, partial moments, nonlinear

JEL Classification: C00