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June 2011 Nonparametric least squares estimation of a multivariate convex regression function
Emilio Seijo, Bodhisattva Sen
Ann. Statist. 39(3): 1633-1657 (June 2011). DOI: 10.1214/10-AOS852

Abstract

This paper deals with the consistency of the nonparametric 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.

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Emilio Seijo. Bodhisattva Sen. "Nonparametric least squares estimation of a multivariate convex regression function." Ann. Statist. 39 (3) 1633 - 1657, June 2011. https://doi.org/10.1214/10-AOS852

Information

Published: June 2011
First available in Project Euclid: 25 July 2011

zbMATH: 0132.38905
MathSciNet: MR2850215
Digital Object Identifier: 10.1214/10-AOS852

Subjects:
Primary: 62G05 , 62G08
Secondary: 62G20

Keywords: consistency , linear program , semidefinite quadratic program , shape restricted estimation , subdifferentials

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • June 2011
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