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2013 | OriginalPaper | Buchkapitel

58. Spline Estimation for a Class of Time Series Variance Model

verfasst von : Xin-qian Wu, Wan-cai Yang, Shu-hong Zhang

Erschienen in: The 19th International Conference on Industrial Engineering and Engineering Management

Verlag: Springer Berlin Heidelberg

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Abstract

A class of nonparametric variance model with weakly stationary linear innovation process is considered in this paper. Based on polynomial spline method, optimal global rate of convergence of the estimator of nonparametric variance function is obtained. The methodology is illustrated by simulation and real data examples.

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Literatur
Zurück zum Zitat Boente G, Ruiz M, Zamar RH (2010) On a robust local estimator for the scale function in heteroscedastic nonparametric regression. Stat Probab Lett 80(15–16):1185–1195CrossRef Boente G, Ruiz M, Zamar RH (2010) On a robust local estimator for the scale function in heteroscedastic nonparametric regression. Stat Probab Lett 80(15–16):1185–1195CrossRef
Zurück zum Zitat Brown LD, Levine M (2007) Variance estimation in nonparametric regression via the difference sequence method. Ann Stat 35(5):2219–2232CrossRef Brown LD, Levine M (2007) Variance estimation in nonparametric regression via the difference sequence method. Ann Stat 35(5):2219–2232CrossRef
Zurück zum Zitat Burman P (1991) Regression function estimation from dependent observations. J Multivar Anal 36(2):263–279CrossRef Burman P (1991) Regression function estimation from dependent observations. J Multivar Anal 36(2):263–279CrossRef
Zurück zum Zitat Cai TT, Levine M, Wang L (2009) Variance function estimation in multivariate nonparametric regression with fixed design. J Multivar Anal 100(1):126–136CrossRef Cai TT, Levine M, Wang L (2009) Variance function estimation in multivariate nonparametric regression with fixed design. J Multivar Anal 100(1):126–136CrossRef
Zurück zum Zitat Dahl CM, Levine M (2006) Nonparametric estimation of volatility models with serially dependent innovations. Stat Probab Lett 76(18):2007–2016CrossRef Dahl CM, Levine M (2006) Nonparametric estimation of volatility models with serially dependent innovations. Stat Probab Lett 76(18):2007–2016CrossRef
Zurück zum Zitat Fan J, Yao Q (2006) Nonlinear time series: nonparametric and parametric methods. Science Press, Beijing, pp 67–77 Fan J, Yao Q (2006) Nonlinear time series: nonparametric and parametric methods. Science Press, Beijing, pp 67–77
Zurück zum Zitat Guo H, Koul HL (2007) Nonparametric regression with heteroscedastic long memory errors. J Stat Plan Inference 137(2):379–404CrossRef Guo H, Koul HL (2007) Nonparametric regression with heteroscedastic long memory errors. J Stat Plan Inference 137(2):379–404CrossRef
Zurück zum Zitat Hall P, Carroll RJ (1989) Variance function estimation in regression: the effect estimation of the mean. J R Stat Soc Ser B 51(1):3–14 Hall P, Carroll RJ (1989) Variance function estimation in regression: the effect estimation of the mean. J R Stat Soc Ser B 51(1):3–14
Zurück zum Zitat Müller HG, Stadtmüller U (1987) Estimation of heteroscedasticity in regression analysis. Ann Stat 15(2):610–625CrossRef Müller HG, Stadtmüller U (1987) Estimation of heteroscedasticity in regression analysis. Ann Stat 15(2):610–625CrossRef
Zurück zum Zitat Stone CJ (1982) Optimal global rates of convergence for nonparametric regression. Ann Stat 10(4):1040–1053CrossRef Stone CJ (1982) Optimal global rates of convergence for nonparametric regression. Ann Stat 10(4):1040–1053CrossRef
Zurück zum Zitat Wang L, Brown LD, Cai TT, Levine M (2008) Effect of mean on variance function estimation in nonparametric regression. Ann Stat 36(2):646–664CrossRef Wang L, Brown LD, Cai TT, Levine M (2008) Effect of mean on variance function estimation in nonparametric regression. Ann Stat 36(2):646–664CrossRef
Zurück zum Zitat Wu X, Yang W (2009) Spline estimation for a nonparametric variance model under dependent innovations. In: Conference proceedings of the 2009 international Institute of Applied Statistics Studies, Sydney Australia, Aussino Academic Publishing House, vol II, pp 2737–2741 Wu X, Yang W (2009) Spline estimation for a nonparametric variance model under dependent innovations. In: Conference proceedings of the 2009 international Institute of Applied Statistics Studies, Sydney Australia, Aussino Academic Publishing House, vol II, pp 2737–2741
Zurück zum Zitat Wu X, Feng A, Tian P (2009a) Spline estimation for nonparametric variance models under dependent observations. J Henan Univ Sci Technol (Nat Sci) 30(5):93–96, 104 (in Chinese) Wu X, Feng A, Tian P (2009a) Spline estimation for nonparametric variance models under dependent observations. J Henan Univ Sci Technol (Nat Sci) 30(5):93–96, 104 (in Chinese)
Zurück zum Zitat Wu X, Tian Z, Wang H (2009b) Polynomial spline estimation for nonparametric (auto-) regressive models. Studia Scientiarum Mathematicarum Hungarica 46(4):515–538CrossRef Wu X, Tian Z, Wang H (2009b) Polynomial spline estimation for nonparametric (auto-) regressive models. Studia Scientiarum Mathematicarum Hungarica 46(4):515–538CrossRef
Zurück zum Zitat Wu X, Yang W, Li S (2011) Spline estimation for nonparametric variance models with linear process innovations. In: Proceedings of the 2011 international conference on consumer electronics, communications and networks, IEEE Press 6:5251–5254 Wu X, Yang W, Li S (2011) Spline estimation for nonparametric variance models with linear process innovations. In: Proceedings of the 2011 international conference on consumer electronics, communications and networks, IEEE Press 6:5251–5254
Metadaten
Titel
Spline Estimation for a Class of Time Series Variance Model
verfasst von
Xin-qian Wu
Wan-cai Yang
Shu-hong Zhang
Copyright-Jahr
2013
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-37270-4_58

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