An optimization interpretation of integration and back-fitting estimators for separable nonparametric models

We provide an optimization interpretation of both back-fitting and integration estimators for additive nonparametric regression. We find that the integration estimator is a projection with respect to a product measure. We also provide further understanding of the back-fitting method.

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Bibliographische Detailangaben
Veröffentlicht in:	Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 1998, Vol.60 (1), p.217-222
Hauptverfasser:	Nielsen, J. P., Linton, O. B.
Format:	Artikel
Sprache:	eng
Schlagworte:	Additive regression models Curse of dimensionality Density estimation Dimensionality reduction Estimation methods Estimators Kernel estimation Least squares Nonparametric models Nonparametric regression Point estimators Regression analysis Statistical models Term weighting Weighting functions
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Beschreibung
Zusammenfassung:	We provide an optimization interpretation of both back-fitting and integration estimators for additive nonparametric regression. We find that the integration estimator is a projection with respect to a product measure. We also provide further understanding of the back-fitting method.
ISSN:	1369-7412 1467-9868
DOI:	10.1111/1467-9868.00120