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 regressi...

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Veröffentlicht in:	IEEE transactions on information theory 2008-02, Vol.54 (2), p.867-874
Hauptverfasser:	Gyorfi, L., Wegkamp, M.
Format:	Artikel
Sprache:	eng
Schlagworte:	Additive noise Applied sciences Cluster analysis Clustering Coding, codes Convergence Counters Data compression Estimates Exact sciences and technology finite-sample bounds Inequalities Inequality Information theory Information, signal and communications theory Least squares approximation least squares estimates Least squares method Multivariate regression Probability distribution Quantization Regression Regression analysis Regression estimation with restriction Sampling, quantization Signal and communications theory Signal representation. Spectral analysis Signal, noise Telecommunications and information theory Temperature Vector quantization Weather forecasting Yield estimation
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Beschreibung
Zusammenfassung:	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.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2007.913565