On Convergence Rates of Convex Regression in Multiple Dimensions

We consider a least squares estimator for estimating a convex function f_*: [0, 1]^d → ℝ with bounded subgradients. A rate at which the sum of squared differences between the estimator and the true function f_* converges to zero is computed. This work sheds light on computing the convergence rate of the multidimensional convex regression estimator.