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Fitting a bivariate additive model by local polynomial regression
Open accessAbstract
While the additive model is a popular nonparametric regression method, many of its theoretical properties are not well understood, especially when the backfitting algorithm is used for computation of the estimators. This article explores those properties when the additive model is fitted by local polynomial regression. Sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given. Asymptotic approximations to the bias and the variance of a homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed. This model is shown to have the same rate of convergence as that of univariate local polynomial regression.
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On the use of generalized additive models in time-series studies of air pollution and health
Dominici, F. (2002) · American Journal of Epidemiology · doi:10.1093/aje/kwf062 · Cited by 728
Metadata
- Authors
- Opsomer, J. D., & Ruppert, D.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1997-02-01
- Volume
- 25
- Issue
- 1
- Pages
- 186-211
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1992272072
- Cited by
- 292
- References
- 0
- FWCI
- 9.40
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Opsomer, J. D., & Ruppert, D. (1997). Fitting a bivariate additive model by local polynomial regression. The Annals of Statistics. https://doi.org/10.1214/aos/1034276626
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
