Quantization for nonparametric regression
Laszlo Gyorfi and Marten Wegkamp
IEEE Transactions on Information Theory
The authors discuss quantization or clustering of non-parametric 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.