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Oracally efficient spline smoothing of nonlinear additive autoregression models with simultaneous confidence band

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  • Song, Qiongxia
  • Yang, Lijian

Abstract

Under weak conditions of smoothness and mixing, we propose spline-backfitted spline (SBS) estimators of the component functions for a nonlinear additive autoregression model that is both computationally expedient for analyzing high dimensional large time series data, and theoretically reliable as the estimator is oracally efficient and comes with asymptotically simultaneous confidence band. Simulation evidence strongly corroborates with the asymptotic theory.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 101 (2010)
Issue (Month): 9 (October)
Pages: 2008-2025

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Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2008-2025

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Related research

Keywords: B spline Confidence band Knots Mixing Oracle efficiency;

References

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  1. Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 487-503.
  3. Roca-Pardinas, Javier & Cadarso-Suarez, Carmen & Tahoces, Pablo G. & Lado, Maria J., 2008. "Assessing continuous bivariate effects among different groups through nonparametric regression models: An application to breast cancer detection," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1958-1970, January.
  4. Zudi Lu & Arvid Lundervold & Dag Tjøstheim & Qiwei Yao, 2007. "Exploring spatial nonlinearity using additive approximation," LSE Research Online Documents on Economics 5401, London School of Economics and Political Science, LSE Library.
  5. Sperlich, Stefan & Tj stheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 197-251, April.
  6. Krivobokova, Tatyana & Kauermann, Goran, 2007. "A Note on Penalized Spline Smoothing With Correlated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1328-1337, December.
  7. Hua Liang & Sally W. Thurston & David Ruppert & Tatiyana Apanasovich & Russ Hauser, 2008. "Additive partial linear models with measurement errors," Biometrika, Biometrika Trust, vol. 95(3), pages 667-678.
  8. Jens Perch Nielsen & Stefan Sperlich, 2005. "Smooth backfitting in practice," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 43-61.
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Cited by:
  1. Efromovich, Sam, 2011. "Nonparametric estimation of the anisotropic probability density of mixed variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 468-481, March.

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