A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting

A Note on Wavelet Estimation of the Derivatives of a Regression Function in a Random Design Setting

We investigate the estimation of the derivatives of a regression function in the nonparametric regression model with random design. New wavelet estimators are developed. Their performances are evaluated via the mean integrated squared error. Fast rates of convergence are obtained for a wide class of...

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Veröffentlicht in:International Journal of Mathematics and Mathematical Sciences 2014, Vol.2014 (2014), p.92-99
1. Verfasser: Chesneau, Christophe
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Convergence
Derivatives
Derivatives (Mathematics)
Estimators
Mathematical analysis
Mathematical models
Multilevel analysis
Nonparametric statistics
Performance evaluation
Probability
Random variables
Regression
Wavelet
Wavelet transforms
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Beschreibung
Zusammenfassung:We investigate the estimation of the derivatives of a regression function in the nonparametric regression model with random design. New wavelet estimators are developed. Their performances are evaluated via the mean integrated squared error. Fast rates of convergence are obtained for a wide class of unknown functions.
ISSN:0161-1712
1687-0425
DOI:10.1155/2014/195765