Nonparametric Least Squares Estimation of a Multivariate Convex Regression Function

2010/03/24 by Emilio Seijo, Seijo, Emilio, Bodhisattva Sen +1 · 5 citations
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1003.4765

openalex publication_date 2010/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. Mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided. We also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization, computation and consistency of its least squares estimator.

Citations

• The Nonparametric Approach to Demand Analysis
• Numerical optimization

Cited by

• Learning and Testing Convex Functions
• Kernel-Based Nonparametric Tests For Shape Constraints
• Convex Regression with a Penalty
• Identifiable Convex-Concave Regression via Sub-gradient Regularised Least Squares
• Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators

Related

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