Spline Estimate of Nonparametric Regression Function under Martingale Difference Errors

Xin Qian Wu; Wan Cai Yang

doi:10.4028/www.scientific.net/AMR.403-408.5239

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 403-408Spline Estimate of Nonparametric Regression...

Spline Estimate of Nonparametric Regression Function under Martingale Difference Errors

Abstract:

Nonparametric regression models with fixed design points and martingale difference errors are considered in this paper. Under mild conditions, optimal global rate of convergence of regression function estimator based on polynomial spline is obtained. Simulation results show that spline method outperforms kernel method at some cases. The regression function is fitted for the CNY/EUR foreign exchange rate series.

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Periodical:

Advanced Materials Research (Volumes 403-408)

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5239-5243

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.403-408.5239

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Online since:

November 2011

Authors:

Xin Qian Wu, Wan Cai Yang

Keywords:

Global Rate of Convergence, Martingale Difference, Regression Function, Spline Estimate

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References

[1] G. Wahba: Bayesian confidence intervals, for the cross-validated smoothing spline, Journal of the Royal Statistical Society, Vol. 45B (1983), pp.133-150.

DOI: 10.1111/j.2517-6161.1983.tb01239.x

Google Scholar

[2] S. Zhou, X. Shen and D.A. Wolfe: Local asymptotics for regression splines and confidence regions, The Annals of Statistics, Vol. 26 (1998), pp.1760-1782.

DOI: 10.1214/aos/1024691356

Google Scholar

[3] W. Mao and L.H. Zhao: Free-knot polynomial splines with confidence intervals, Journal of the Royal Statistical Society, Vol. 65B (2003), pp.901-919.

DOI: 10.1046/j.1369-7412.2003.00422.x

Google Scholar

[4] J.Z. Huang: Local asymptotics for polynomial spline regression, The Annals of Statistics, Vol. 31 (2003), pp.1600-1635.

Google Scholar

[5] P. Burman: Regression function estimation from dependent observations, Journal of Multivariate Analysis, Vol. 36 (1991), pp.263-279.

DOI: 10.1016/0047-259x(91)90061-6

Google Scholar

[6] X. Wu: Spline estimate of regressive function under linear process errors, Journal of Henan University of Science and Technology (Natural Science), Vol. 31 No. 5 (2010), pp.94-97. (in Chinese).

Google Scholar

[7] X. Wu, W. Yang and Y. Han, Spline estimation for nonparametric regression with linear process errors, in: Data Processing and Quantitative Economy Modeling-Conference Proceedings of the 3rd International Institute of Statistics & Management Engineering Symposium, edited by K. Zhu, and H. Zhang, Aussino Academic Publishing House, Sydney Australia (2010).

Google Scholar

[8] X. Wu and W. Yang, Spline estimate of nonlinear trend for time series, in: 2010 First ACIS International Symposium on Cryptography, and Network Security, Data Mining and Knowledge Discovery, E-Commerce and Its Applications, and Embedded Systems, Qinhuangdao, Hebei, China. IEEE Inc. (2010).

DOI: 10.1109/cdee.2010.28

Google Scholar

[9] J. Wang: Modelling time trend via spline confidence band, Annals of The Institute of Statistical Mathematics, Vol. 62 (2010), pp.1-27.

Google Scholar

[10] G. -L. Fan and H. -Y. Liang: Empirical likelihood inference for semiparametric model with linear process errors, Journal of the Korean Statistical Society, Vol. 39 (2010), pp.55-65.

DOI: 10.1016/j.jkss.2009.04.001

Google Scholar