## 留言板

 引用本文: 李林元, 肖益民. 强相关数据回归函数的小波估计[J]. 应用数学和力学, 2006, 27(7): 789-798.
LI Lin-yuan, XIAO Yi-min. Wavelet-Based Estimators of the Mean Regression Function With Long Memory Date[J]. Applied Mathematics and Mechanics, 2006, 27(7): 789-798.
 Citation: LI Lin-yuan, XIAO Yi-min. Wavelet-Based Estimators of the Mean Regression Function With Long Memory Date[J]. Applied Mathematics and Mechanics, 2006, 27(7): 789-798.

## 强相关数据回归函数的小波估计

###### 作者简介:李林元(1965- ),男,江苏人,副教授,博士(联系人.E-mail:linyuan@math.unh.edu).
• 中图分类号: O212.7

## Wavelet-Based Estimators of the Mean Regression Function With Long Memory Date

• 摘要: 讨论了在强相关数据情形下对回归函数的小波估计，并且给出了估计量的均方误差的一个渐近展开表示式． 对研究估计量的优劣，所推导的近似表示式显得非常重要．对一般的回归函数核估计，如果回归函数不是充分光滑，这个均方误差表示式并不成立A·D2但对小波估计，即使回归函数间断连续，这个均方误差表示式仍然成立．因此，小波估计的收敛速度要比核估计来得快，从而小波估计在某种程度上改进了现有的核估计．
•  [1] Hart J D.Kernel regression estimation with time series errors[J].J Roy Statist Soc,Ser B,1991,53：173—187. [2] Tran L T,Roussas G G,Yakowitz S,et al.Fixed-design regression for linear time series[J].Ann Statist,1996,24：975—991. [3] Truong Y K,Patil P N.Asymptotics for wavelet based estimates of piecewise smooth regression for stationary time series[J].Ann Inst Statist Math,2001,53：159—178. [4] Beran J.Statistics for Long Memory Processes[M].New York:Chapman and Hall,1994. [5] Hall P,Hart J D.Nonparametric regression with long-range dependence[J].Stochastic Process Appl,1990,36：339—351. [6] Robinson P M,Hidalgo F J.Time series regression with long-range dependence[J].Ann Statist,1997,25：77—104. [7] Csorgo S,Mielniczuk J.Nonparametric regression under long-range dependent normal errors[J].Ann Statist,1995,23：1000—1014. [8] Robinson P M.Large-sample inference for nonparametric regression with dependent errors[J].Ann Statist,1997,25：2054—2083. [9] Hardle W,Kerkyacharian G,Picard D,et al.Wavelets, Approximation and Statistical Applications[M].Lecture Notes in Statistics, 129.New York:Springer-Verlag,1998. [10] Donoho D L,Johnstone I M.Minimax estimation via wavelet shrinkage[J].Ann Statist,1998,26：879—921. [11] Donoho D L,Johnstone I M,Kerkyacharian G,et al.Wavelet shrinkage: asymptopia? (with discussion)[J].J Roy Statist Soc,Ser B,1995,57：301—369. [12] Donoho D L,Johnstone I M,Kerkyacharian G,et al.Density estimation by wavelet thresholding[J].Ann Statist,1996,24：508—539. [13] Hall P,Patil P.Formulae for mean integated squared error of non-linear waveletbased density estimators[J].Ann Statist,1995,23：905—928. [14] Hall P,Patil P.On the choice of smoothing parameter, threshold and truncation in nonparametric regression by nonlinear wavelet methods[J].J Roy Statist Soc,Ser B,1996,58：361—377. [15] Hall P,Patil P.Effect of threshold rules on performance of wavelet-based curve estimators[J].Statistic Sinica,1996,6:331—345. [16] Johnstone I M.Wavelet threshold estimators for correlated data and inverse problems: Adaptivity results[J].Statistica Sinica,1999,9：51—83. [17] Johnstone I M,Silverman B W.Wavelet threshold estimators for data with correlated noise[J].J Roy Statist Soc,Ser B,1997,59：319—351. [18] Wang Y.Function estimation via wavelet shrinkage for long-memory data[J].Ann Statist,1996,24：466—484. [19] Daubechies I.Ten Lectures on Wavelets[M].Philadelphia:SIAM,1992. [20] Cohen A,Daubechies I,Vial P.Wavelets on the interval and fast wavelet transforms[J].Appl Comput Harm Anal,1993,1：54—82. [21] Abry P,Veitch D.Wavelet analysis of long-range-dependent traffic[J].IEEE Trans on Inform Theory,1998,44：2—15. [22] Delbeke L,Van Assche Walter.A wavelet based estimator for the parameter of selfsimilarity of fractional Brownian motion[A].In:3rd International Conference on Approximation and Optimization in the Caribbean[C].Puebla:1995,Soc Mat Mexicana,M′exico:Aportaciones Mat. Comun 24,1998,65—76. [23] Fox R,Taqqu M.Noncentral limit theorems for quadratic forms in random variables having long-range dependence[J].Ann Probab,1985,13：428—446. [24] Mojor P.Multiple Wiener-It Integrals[M].Lect Notes in Math 849,New York:Springer-Verlag,1981. [25] Durrett R.Probability: Theorey and Examples[M].Second Edition:Duxbury Press，1996.

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##### 出版历程
• 收稿日期:  2005-01-17
• 修回日期:  2006-04-09
• 刊出日期:  2006-07-15

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