Smoothing noisy data with tapered coiflets series

被引：0
|
作者：
Antoniadis, A
机构：
来源：
SCANDINAVIAN JOURNAL OF STATISTICS | 1996年 / 23卷 / 03期
关键词：
curve smoothing; multi-resolution analysis; non-parametric regression; penalized least-squares; splines; wavelets;
D O I：
暂无
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
This paper is concerned with an orthogonal wavelet series estimator of an unknown smooth regression function observed with noise on a bounded interval. A penalized least-squares approach is adopted and our method uses the specific asymptotic interpolating properties of the wavelet approximation generated by a particular wavelet basis, Daubechie's coiflets. A simple procedure is described to estimate the smoothing parameter of the penalizing functional and conditions are given for the estimator to attain optimal convergence rates in the integrated mean square sense as the sample size increases to infinity. The results are illustrated with simulated and real examples and a comparison with other non-parametric smoothers is made.
引用
收藏
页码：313 / 330
页数：18
相关论文
共 50 条
  • [11] The complexity of model classes, and smoothing noisy data
    Bartlett, Peter L.
    Kulkarni, Sanjeev R.
    [J]. Systems and Control Letters, 1998, 34 (03): : 133 - 140
  • [12] SMOOTHING NOISY DATA BY 2 EQUIVALENT TECHNIQUES
    THOMASAGNAN, C
    [J]. DATA ANALYSIS, LEARNING SYMBOLIC AND NUMERIC KNOWLEDGE, 1989, : 247 - 256
  • [13] Approximation by smoothing variational vector splines for noisy data
    Kouibia, A.
    Pasadas, M.
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 211 (02) : 213 - 222
  • [14] Constrained Smoothing of Noisy Data Using Splines in Tension
    Nicholas A. Teanby
    [J]. Mathematical Geology, 2007, 39 : 419 - 434
  • [15] Smoothing noisy data via regularization: statistical perspectives
    Gu, Chong
    [J]. INVERSE PROBLEMS, 2008, 24 (03)
  • [16] Constrained smoothing of noisy data using splines in tension
    Teanby, Nicholas A.
    [J]. MATHEMATICAL GEOLOGY, 2007, 39 (04): : 419 - 434
  • [17] OPTIMAL SMOOTHING OF NOISY DATA USING SPLINE FUNCTIONS
    UTRERAS, F
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1981, 2 (03): : 349 - 362
  • [18] Smoothing methodology for time series data
    Khosrowshahi, F.
    [J]. CHALLENGES, OPPORTUNITIES AND SOLUTIONS IN STRUCTURAL ENGINEERING AND CONSTRUCTION, 2010, : 933 - 937
  • [19] Convergent smoothing and segmentation of noisy range data in multiscale space
    Adams, Martin
    Fan, Tang
    Wijesoma, Wijerupage Sardha
    Sok, Chhay
    [J]. IEEE TRANSACTIONS ON ROBOTICS, 2008, 24 (03) : 746 - 753
  • [20] THE DISCRETE K-FUNCTIONAL AND SPLINE SMOOTHING OF NOISY DATA
    RAGOZIN, DL
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1985, 22 (06) : 1243 - 1254
12345