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We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-squares estimator on finite-dimensional vector spaces. We give upper and lower bounds on these quantities that are nonasymptotic and optimal to first order, allowing the dimension to depend on sample size. These bounds show the equivalence between the true and empirical excess risks when, among other things, the least-squares estimator is consistent in sup-norm with the projection of the regression function onto the considered model. Consistency in the sup-norm is then proved for suitable histogram models and more general models of piecewise polynomials that are endowed with a localized basis structure.

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Project Euclid (Hosted at Cornell University Library)  

Autor(es)

Saumard, Adrien - 

Id.: 55207165

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveLeast -  squares regression - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2012 Institute of Mathematical Statistics

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 1935-7524

Fecha de contribución: 26-ene-2013

Contacto:

Localización:
* Electron. J. Statist. 6 (2012), 579-655
* doi:10.1214/12-EJS679

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