A More Efficient Algorithm for Convex Nonparametric Least Squares

Abstract

Convex Nonparametric Least Squares (CNLS) is a nonparametric regression method that does not require a priori specification of the functional form. The CNLS problem is solved by mathematical programming techniques; however, since the CNLS problem size grows quadratically as a function of the number of observations, standard Quadratic Programming (QP) and Nonlinear Programming (NLP) algorithms are inadequate for handling large samples, and the computational burdens become significant even for relatively small samples. This study proposes a generic algorithm that improves the computational performance in small samples and is able to solve problems that are currently unattainable. A Monte Carlo simulation is performed to evaluate the performance of six variants of the proposed algorithm. These experimental results indicate that a particular variant is most efficient given the sample size and the dimensionality. The computational benefits of the new algorithm are demonstrated by an empirical application that proved insurmountable for the standard QP and NLP algorithms.