• Corpus ID: 219259999

Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators

  title={Convex Regression in Multidimensions: Suboptimality of Least Squares Estimators},
  author={Gil Kur and Fuchang Gao and Adityanand Guntuboyina and Bodhisattva Sen},
  journal={arXiv: Statistics Theory},
The least squares estimator (LSE) is shown to be suboptimal in squared error loss in the usual nonparametric regression model with Gaussian errors for $d \geq 5$ for each of the following families of functions: (i) convex functions supported on a polytope (in fixed design), (ii) bounded convex functions supported on a polytope (in random design), and (iii) convex Lipschitz functions supported on any convex domain (in random design). For each of these families, the risk of the LSE is proved to… 
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