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A Central Limit Theorem for Local Polynomial Backfitting Estimators

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  • Wand, M. P.

Abstract

Additive models based on backfitting estimators are among the most important recent contributions to modern statistical modelling. However, the statistical properties of backfitting estimators have received relatively little attention. Recently, J.-D. Opsomer and D. Ruppert (1997,Ann. Statist.25, 186-211; 1998,J. Amer. Statist. Assoc.93, 605-619) and J.-D. Opsomer (1997, preprint 96-12, Department of statistics, Iowa State University) derived their mean squared error properties in the case of local polynomial smoothers. In this paper the asymptotic distributional behaviour of backfitting estimators is investigated.

Suggested Citation

  • Wand, M. P., 1999. "A Central Limit Theorem for Local Polynomial Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 57-65, July.
    • Handle: RePEc:eee:jmvana:v:70:y:1999:i:1:p:57-65
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    Citations

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    Cited by:

    1. Zhang, Chunming & Li, Jialiang & Meng, Jingci, 2008. "On Stein's lemma, dependent covariates and functional monotonicity in multi-dimensional modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2285-2303, November.
    2. Takuma Yoshida & Kanta Naito, 2014. "Asymptotics for penalised splines in generalised additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 269-289, June.
    3. Graciela Boente & Alejandra Martínez & Matías Salibián-Barrera, 2017. "Robust estimators for additive models using backfitting," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 744-767, October.
    4. Cai, Zongwu & Fan, Jianqing, 2000. "Average Regression Surface for Dependent Data," Journal of Multivariate Analysis, Elsevier, vol. 75(1), pages 112-142, October.
    5. Abhijit Mandal, 2020. "An optimal test for the additive model with discrete or categorical predictors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1397-1417, December.

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