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Quantization for Nonparametric Regression

The authors discuss quantization or clustering of nonparametric regression estimates. The main tools developed are oracle inequalities for the rate of convergence of constrained least squares estimates. These inequalities yield fast rates for both nonparametric (unconstrained) least squares regression and clustering of partition regression estimates and plug-in empirical quantizers. The bounds on the rate of convergence generalize known results for bounded errors to subGaussian, too.