Journal
ANNALS OF STATISTICS
Volume 39, Issue 3, Pages 1633-1657Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/10-AOS852
Keywords
Consistency; linear program; semidefinite quadratic program; shape restricted estimation; subdifferentials
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Funding
- NSF [DMS-09-06597]
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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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