The DOI matches its Crossref record; 41 of the 41 references it cites were found in a registry or an index.
Linear Smoothers and Additive Models
Open accessAbstract
We study linear smoothers and their use in building nonparametric regression models. In the first part of this paper we examine certain aspects of linear smoothers for scatterplots; examples of these are the running-mean and running-line, kernel and cubic spline smoothers. The eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother, and several other topics such as the number of degrees of freedom of a smoother are discussed. In the second part of the paper we describe how linear smoothers can be used to estimate the additive model, a powerful nonparametric regression model, using the "back-fitting algorithm." We show that backfitting is the Gauss-Seidel iterative method for solving a set of normal equations associated with the additive model. We provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers.
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Cites
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Solving Least Squares Problems
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Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting
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Cited by
Dormann, C. F., Elith, J., Bacher, S., Buchmann, C., Carl, G., Carré, G., Marquéz, J. R. G., Gruber, B., Lafourcade, B., Leitão, P. J., et al. (2013) · Ecography · doi:10.1111/j.1600-0587.2012.07348.x · Cited by 9,998
Friedman, J., Hastie, T., & Tibshirani, R. (2000) · The Annals of Statistics · doi:10.1214/aos/1016218223 · Cited by 6,884
Self-citationSome Tools for Functional Data Analysis
Ramsay, J. O., & Dalzell, C. J. (1991) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1991.tb01844.x · Cited by 939
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
Model Choice in Time Series Studies of Air Pollution and Mortality
Peng, R. D., Dominici, F., & Louis, T. A. (2006) · Journal of the Royal Statistical Society Series A: Statistics in Society · doi:10.1111/j.1467-985x.2006.00410.x · Cited by 583
Metadata
- Authors
- Buja, A., Hastie, T., & Tibshirani, R.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1989-06-01
- Volume
- 17
- Issue
- 2
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2162430620
- Cited by
- 989
- References
- 41
- FWCI
- 21.13
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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