平稳遍历函数型非参数递归M估计的收敛速度
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摘要
文章基于平稳遍历函数型数据,构造非参数回归算子的递归M估计,在一定条件下建立了递归估计量的几乎完全一致收敛速度,推广了现有文献中的相关结果。
In this paper, recursive method is adopted to study recursive M-estimation of functional nonparametric regression model for functional stationary ergodic data. Under some conditions, the uniform almost complete convergence rate of regression operator estimation is established. The results generalize the relevant results in the existing literature.
In this paper, recursive method is adopted to study recursive M-estimation of functional nonparametric regression model for functional stationary ergodic data. Under some conditions, the uniform almost complete convergence rate of regression operator estimation is established. The results generalize the relevant results in the existing literature.
引文
[1] FERRATY F,VIEU P.Nonparametric functional data analysis[M].New York:Springer,2006.
[2] HUBER P J.Robust estimation of a location parameter[J].Annals of Mathematical Statistics,1964,35(1):73-101.
[3] HUBER,PETER J.Robust regression:asymptotics,conjectures and Monte Carlo[J].Annals of Statistics,1973,1(5):799-821.
[4] BOENTE G,FRAIMAN R.Robust nonparametric regression estimation for dependent observations[J].Journal of Multivariate Analysis,1989,29(2):180-198.
[5] CRAMBES C,DESOL L,LAKSACI A.Robust nonparametric estimation for functional data[J].Journal of Nonparametric Statistics,2008,20(7):573-598.
[6] AZZEDINE N,LAKSACI A,OULD-SAID E.On robust nonparametric regression estimation for a functional regressor[J].Statistics & Probability Letters,2008,78(18):3216-3221.
[7] ATTOUCH M K,GHERIBALLAH A,Laksaci A.Robust nonparametric estimation for functional spatial regression[J].Journal of Statistical Planning & Inference,2010,140(7):1656-1670.
[8] 程伟,凌能祥.基于相依函数型数据非参数回归函数的稳健核估计[J].数学杂志,2011,31(2):352-356.
[9] 范剑青,姚琦伟.非线性时间序列:建模、预报及应用[M].北京:高等教育出版社,2005:19-45.
[10] LAIB N,LOUANI D.Nonparametric kernel regression estimation for functional stationary ergodic data:asymptotic properties[J].Journal of Multivariate Analysis,2010,101(10):2266-2281.
[11] LAIB N,LOUANI D.Rates of strong consistencies of the regression function estimator for functional stationary ergodic data[J].The Journal of Statistical Planning and Inference,2011,141(1):359-372.
[12] GHERIBALLAH A,LAKSACI A,SEKKAL S.Nonparametric M-regression for functional ergodic data[J].Statistics and Probability Letters,2013,83(3):902-908.
[13] AMIRI A.Recursive regression estimators with application to nonparametric prediction[J].Journal of Nonparametric Statistics,2012,24(1):169-186.
[14] AMIRI A,CRAMBES C,THIAM B.Recursive estimation of nonparametric regression with functional covariate[J].Computational Statistics and Data Analysis,2012,69(1):154-172.
[15] AMIRI A,THIAM B.Consistency of the recursive nonparametric regression estimation for dependent functional data[J].Journal of Nonparametric Statistics,2014,26(3):471-487.
[16] 杨艳,凌能祥,王娟,等.非参数函数型递归核估计的收敛速度[J].合肥工业大学学报(自然科学版),2014(12):1528-1531.
[17] COLLOMB G,WOLFGANG H.Strong uniform convergence rates in robust nonparametric time series analysis and prediction:kernel regression estimation from dependent observations[J].Stochastic Processes & Their Applications,1986,23(1):77-89.
[2] HUBER P J.Robust estimation of a location parameter[J].Annals of Mathematical Statistics,1964,35(1):73-101.
[3] HUBER,PETER J.Robust regression:asymptotics,conjectures and Monte Carlo[J].Annals of Statistics,1973,1(5):799-821.
[4] BOENTE G,FRAIMAN R.Robust nonparametric regression estimation for dependent observations[J].Journal of Multivariate Analysis,1989,29(2):180-198.
[5] CRAMBES C,DESOL L,LAKSACI A.Robust nonparametric estimation for functional data[J].Journal of Nonparametric Statistics,2008,20(7):573-598.
[6] AZZEDINE N,LAKSACI A,OULD-SAID E.On robust nonparametric regression estimation for a functional regressor[J].Statistics & Probability Letters,2008,78(18):3216-3221.
[7] ATTOUCH M K,GHERIBALLAH A,Laksaci A.Robust nonparametric estimation for functional spatial regression[J].Journal of Statistical Planning & Inference,2010,140(7):1656-1670.
[8] 程伟,凌能祥.基于相依函数型数据非参数回归函数的稳健核估计[J].数学杂志,2011,31(2):352-356.
[9] 范剑青,姚琦伟.非线性时间序列:建模、预报及应用[M].北京:高等教育出版社,2005:19-45.
[10] LAIB N,LOUANI D.Nonparametric kernel regression estimation for functional stationary ergodic data:asymptotic properties[J].Journal of Multivariate Analysis,2010,101(10):2266-2281.
[11] LAIB N,LOUANI D.Rates of strong consistencies of the regression function estimator for functional stationary ergodic data[J].The Journal of Statistical Planning and Inference,2011,141(1):359-372.
[12] GHERIBALLAH A,LAKSACI A,SEKKAL S.Nonparametric M-regression for functional ergodic data[J].Statistics and Probability Letters,2013,83(3):902-908.
[13] AMIRI A.Recursive regression estimators with application to nonparametric prediction[J].Journal of Nonparametric Statistics,2012,24(1):169-186.
[14] AMIRI A,CRAMBES C,THIAM B.Recursive estimation of nonparametric regression with functional covariate[J].Computational Statistics and Data Analysis,2012,69(1):154-172.
[15] AMIRI A,THIAM B.Consistency of the recursive nonparametric regression estimation for dependent functional data[J].Journal of Nonparametric Statistics,2014,26(3):471-487.
[16] 杨艳,凌能祥,王娟,等.非参数函数型递归核估计的收敛速度[J].合肥工业大学学报(自然科学版),2014(12):1528-1531.
[17] COLLOMB G,WOLFGANG H.Strong uniform convergence rates in robust nonparametric time series analysis and prediction:kernel regression estimation from dependent observations[J].Stochastic Processes & Their Applications,1986,23(1):77-89.