Please use this identifier to cite or link to this item: https://doi.org/10.3150/09-BEJ183
Title: A note on the backfitting estimation of additive models
Authors: Yingcun, X. 
Keywords: Additive model
Backfitting algorithm
Convergence of algorithm
Kernel smoothing
Issue Date: Nov-2009
Citation: Yingcun, X. (2009-11). A note on the backfitting estimation of additive models. Bernoulli 15 (4) : 1148-1153. ScholarBank@NUS Repository. https://doi.org/10.3150/09-BEJ183
Abstract: The additive model is one of the most popular semi-parametric models. The backfitting estimation (Buja, Hastie and Tibshirani, Ann. Statist. 17 (1989) 453-555) for the model is intuitively easy to understand and theoretically most efficient (Opsomer and Ruppert, Ann. Statist. 25 (1997) 186-211); its implementation is equivalent to solving simple linear equations. However, convergence of the algorithm is very difficult to investigate and is still unsolved. For bivariate additive models, Opsomer and Ruppert (Ann. Statist. 25 (1997) 186-211) proved the convergence under a very strong condition and conjectured that a much weaker condition is sufficient. In this short note, we show that a weak condition can guarantee the convergence of the backfitting estimation algorithm when Nadaraya-Watson kernel smoothing is used. © 2009 ISI/BS.
Source Title: Bernoulli
URI: http://scholarbank.nus.edu.sg/handle/10635/104956
ISSN: 13507265
DOI: 10.3150/09-BEJ183
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