pyStoNED: A Python package for convex regression and frontier estimation

Sheng Dai, Yu-Hsueh Fang, Chia-Yen Lee, Timo Kuosmanen

Research output: Contribution to conferencePaperScientific


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 the 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 powerful, reliable, and fully open access computational package has 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 the 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 the estimation of frontier cost and production functions.
Original languageEnglish
Publication statusPublished - Oct 2021
MoE publication typeNot Eligible
EventInternational Conference on Decision and Data Envelopment Analysis - Virtual, Online
Duration: 27 Oct 202028 Oct 2021
Conference number: 13


ConferenceInternational Conference on Decision and Data Envelopment Analysis
Abbreviated titleDDEA
CityVirtual, Online
Internet address


  • multivariate convex regression
  • nonparametric least squares
  • frontier estimation
  • efficiency analysis
  • stochastic noise
  • python


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