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Asymptotic Properties of Backfitting Estimators (1998)
| Venue: | Journal of Multivariate Analysis |
| Citations: | 33 - 3 self |
BibTeX
@ARTICLE{Opsomer98asymptoticproperties,
author = {Jean D. Opsomer},
title = {Asymptotic Properties of Backfitting Estimators},
journal = {Journal of Multivariate Analysis},
year = {1998},
volume = {73},
pages = {166--179}
}
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Abstract
When additive models with more than two covariates are fitted with the backfitting algorithm proposed by Buja et al. [2], the lack of explicit expressions for the estimators makes study of their theoretical properties cumbersome. Recursion provides a convenient way to extend existing theoretical results for bivariate additive models to models of arbitrary dimension. In the case of local polynomial regression smoothers, recursive asymptotic bias and variance expressions for the backfitting estimators are derived. The estimators are shown to achieve the same rate of convergence as those of univariate local polynomial regression. In the case of independence between the covariates, non-recursive bias and variance expressions, as well as the asymptotically optimal values for the bandwidth parameters, are provided. 1 Introduction The additive model, originally suggested by Friedman and Stuetzle [4], assumes that the conditional expectation function of the dependent variable can be written a...
Keyphrases
backfitting estimator asymptotic property variance expression additive model univariate local polynomial regression explicit expression theoretical result bandwidth parameter convenient way recursive asymptotic bias bivariate additive model theoretical property non-recursive bias optimal value arbitrary dimension dependent variable local polynomial regression smoother conditional expectation function
