Nonparametric least squares estimation of a multivariate convex regression function
The Annals of Statistics · 2011 · Volume 39 · Issue 3
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.
Keywords
62G05, 62G08, 62G20, consistency, linear program, semidefinite quadratic program, shape restricted estimation, subdifferentials
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