基于LENQD序列的线性过程误差回归函数小波估计的Berry-Esseen界

Berry-Esseen bound of wavelet estimator for regression model with linear process errors generated by LENQD sequence

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Abstract: Based on linear process random errors generated by a LENQD random sequence, the wavelet estimator of nonparametric fixed design regression model is considered.By the characteristic function inequality and moment inequality of LENQD random sequence, the Berry-Esseen bounds of the wavelet estimator for unknown regression function are obtained. And by choosing some suitable constants, their bounds can reach $O(n^{-\frac{1}{6}})$ .

Key words: Fixed design regression, Linear process random errors, LENQD random sequence, Wavelet estimator, Berry-Esseen bound

CLC Number:

O212.7

LI Yong-Ming. Berry-Esseen bound of wavelet estimator for regression model with linear process errors generated by LENQD sequence[J].Acta mathematica scientia,Series A, , (): 0-0.

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[1]Georgiev A A.Local properties of function fitting estimates with application to system identication[J].Mathematical statistics and applications, 1985, B ((Bad Tatz-mannsdorf, 1983)):141-151 [2]Georgiev A A.Consistent nonparametric multiple regression: the fixed design case[J].J Multivariate Anal, 1988, 25(1):100-110 [3]Roussas G G, Tran L T, Ioannides D A.Fixed design regression for time series: Asymptotic normality[J].J Multivariate Anal, 1992, 40(2):262-291 [4]杨善朝, 李永明.强混合样本下回归加权估计的一致渐近正态性[J].数学学报, 2006, 49A(5):1163-1170 [5]Yang S C.Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples[J].Stat Probab Lett, 2003, 62(2):101-110 [6]Liang H Y, Li Y Y.A Berry-Esseen type bound of regression estimator based on linear process errors[J].J Korean Math Soc, 2008, 45(6):1753-1767 [7]item Ding L W, Chen P Y, Li Y M.Berry-Esseen bounds of weighted kernel estimator for a nonparametric regression model based on linear process errors under a LNQD sequence[J].J Inequal Appl, 2018, 2018(2018:10):1-12 [8]Antoniadis A, Gregoire G, Mckeague I W.Wavelet methods for curve estimation[J].J Amer Stat Assoc, 1994, 89(428):1340-1352 [9]薛留根.混合误差下回归函数小波估计的一致收敛速度[J].数学物理学报, 2002, 22(4):528-535 [10]孙燕, 柴根象.固定设计下混合序列回归函数小波估计[J].数学物理学报, 2004, 24A(5):597-606 [11]Liang H Y, Qi Y Y.Asymptotic normality of wavelet estimator of regression function under NA assumptions[J].Bull Korean Math Soc, 2007, 44(2):247-257 [12]李永明, 尹长明, 韦程东.varphi

混 合 误 差 下 回 归 函 数 小 波 估 计 的 渐 近 正 态 性 [J] . 应 用 数 学 学 报, 2008, 31 (6) : 1016 - 1055 [13] 李 永 明, 韦 程 东 . 强 混 合 误 差 回 归 函 数 小 波 估 计 的 B e r r y - E s s e e n - 界 [J] . 数 学 物 理 学 报, 2009, 29 A (5) : 1453 - 1463 [14] L i Y M, W e i C D, X i n G D . B e r r y - E s s e e n b o u n d s o f w a v e l e t e s t i m a t o r i n a r e g r e s s i o n w i t h l i n e a r p r o c e s s e r r o r s [J] . S t a t P r o b a b L e t t, 2011, 81 (1) : 103 - 111 [15] 李 永 明, 郭 建 华, 杨 善 朝 . 一 类 混 合 序 列 生 成 的 线 性 过 程 误 差 半 参 数 回 归 模 型 小 波 估 计 的 B e r r y - E s s e e n - 界 [J] . 应 用 数 学 学 报, 2013, 36 (6) : 1021 - 1036 [16] D i n g L W, L i Y M . T h e B e r r y - E s s e e n b o u n d s o f w a v e l e t e s t i m a t o r f o r r e g r e s s i o n m o d e l w h o s e e r r o r s f o r m a l i n e a r p r o c e s s w i t h a

$混合误差下回归函数小波估计的渐近正态性[J].应用数学学报, 2008, 31(6):1016-1055 [13]李永明, 韦程东.强混合误差回归函数小波估计的Berry-Esseen-界[J].数学物理学报, 2009, 29A(5):1453-1463 [14]Li Y M, Wei C D, Xin G D.Berry-Esseen bounds of wavelet estimator in a regression with linear process errors[J].Stat Probab Lett, 2011, 81(1):103-111 [15]李永明, 郭建华, 杨善朝.一类混合序列生成的线性过程误差半参数回归模型小波估计的Berry-Esseen-界[J].应用数学学报, 2013, 36(6):1021-1036 [16]Ding L W, Li Y M.The Berry-Esseen bounds of wavelet estimator for regression model whose errors form a linear process with a$ \rho$-mixing[J].J Inequal Appl, 2016, 2016(2016:107):1-12 [17]Ding L W, Chen P Y, Li Y M.Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples[J].Stat Pap, 2020, 61(6):2331-2349 [18]Li Y M, Pang W C, Feng Z Q, Li N Y.On the linearly extended negative quadrant dependent random variables and its inequalities[J].Commun Stat Theor M, 2022, Published online(DOI: 10.1080/03610926.2022.2068600):1-14 [19]Petrov V V.Limit Theory for probability theory.[J].Oxford University Press, 1995, New York(0):1-273

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[1]	LI Yong-Ming, WEI Cheng-Dong. Berry-Esseen Bounds for Wavelet Estimator of Regression Function under Strong Mixing Process [J]. Acta mathematica scientia,Series A, 2009, 29(5): 1453-1463.
[2]	Lu Chuanrong; Qiu Jin. Strong Approximations of Linear Processes [J]. Acta mathematica scientia,Series A, 2007, 27(2): 309-313.
[3]	Li Yunxia. Precise Asymptotics in the Law of Large Numbers of Moving-average Processes [J]. Acta mathematica scientia,Series A, 2006, 26(5): 675-687.
[4]	SUN Yan, CHAI Gen-Xiang. Nonparametric Wavelet Estimation of a Fixed Designed Regression Function [J]. Acta mathematica scientia,Series A, 2004, 4(5): 597-606.
[5]	XUE Liu-Gen. Uniform Convergence Rates of the Wavelet Estimator of Regression Function Under Mixing Error [J]. Acta mathematica scientia,Series A, 2002, 22(4): 528-535.