pyStoNED: A Python Package for Convex Regression and Frontier Estimation

Abstract

Shape-constrained nonparametric regression is a growing area in econometrics, statistics, operations research, machine learning, and related fields. In the field of productivity and efficiency analysis, recent developments in multivariate convex regression and related techniques such as convex quantile regression and convex expectile regression have bridged the long-standing gap between the conventional deterministic-nonparametric and stochastic-parametric methods. Unfortunately, the heavy computational burden and the lack of a powerful, reliable, and fully open-access computational package have slowed down the diffusion of these advanced estimation techniques to the empirical practice. The purpose of the Python package pyStoNED is to address this challenge by providing a freely available and user-friendly tool for multivariate convex regression, convex quantile regression, convex expectile regression, isotonic regression, stochastic nonparametric envelopment of data, and related methods. This paper presents a tutorial of the pyStoNED package and illustrates its application, focusing on estimating frontier cost and production functions.