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强相关数据回归函数的小波估计

李林元 肖益民

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.
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

详细信息
    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. doi: 10.1214/aos/1032526952
    [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. doi: 10.1023/A:1017928823619
    [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. doi: 10.1016/0304-4149(90)90100-7
    [6] Robinson P M,Hidalgo F J.Time series regression with long-range dependence[J].Ann Statist,1997,25:77—104. doi: 10.1214/aos/1034276622
    [7] Csorgo S,Mielniczuk J.Nonparametric regression under long-range dependent normal errors[J].Ann Statist,1995,23:1000—1014. doi: 10.1214/aos/1176324633
    [8] Robinson P M.Large-sample inference for nonparametric regression with dependent errors[J].Ann Statist,1997,25:2054—2083. doi: 10.1214/aos/1069362387
    [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. doi: 10.1214/aos/1024691081
    [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. doi: 10.1214/aos/1032894451
    [13] Hall P,Patil P.Formulae for mean integated squared error of non-linear waveletbased density estimators[J].Ann Statist,1995,23:905—928. doi: 10.1214/aos/1176324628
    [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. doi: 10.1111/1467-9868.00071
    [18] Wang Y.Function estimation via wavelet shrinkage for long-memory data[J].Ann Statist,1996,24:466—484. doi: 10.1214/aos/1032894449
    [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. doi: 10.1006/acha.1993.1005
    [21] Abry P,Veitch D.Wavelet analysis of long-range-dependent traffic[J].IEEE Trans on Inform Theory,1998,44:2—15. doi: 10.1109/18.650984
    [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. doi: 10.1214/aop/1176993001
    [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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