Non-uniform Randomized Sampling for Multivariate Approximation by High Order Parzen Windows

被引：5
|
作者：
Zhou, Xiang-Jun [1 ,2 ]
Shi, Lei [1 ,2 ]
Zhou, Ding-Xuan [3 ]
机构：
[1] Univ Sci & Technol China, Joint Adv Res Ctr Suzhou, Suzhou 215123, Jiangshu, Peoples R China
[2] City Univ Hong Kong, Suzhou 215123, Jiangshu, Peoples R China
[3] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
来源：
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2011年 / 54卷 / 03期
关键词：
multivariate approximation; Sobolev spaces; non-uniform randomized sampling; high order Parzen windows; convergence rates; RECONSTRUCTION;
D O I：
10.4153/CMB-2011-029-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider approximation of multivariate functions in Sobolev spaces by high order Parzen windows in a non-uniform sampling setting. Sampling points are neither i.i.d. nor regular, but are noised from regular grids by non-uniform shifts of a probability density function. Sample function values at sampling points are drawn according to probability measures with expected values being values of the approximated function. The approximation orders are estimated by means of regularity of the approximated function, the density function, and the order of the Parzen windows, under suitable choices of the scaling parameter.
引用
收藏
页码：566 / 576
页数：11
相关论文
共 50 条
  • [41] Non-uniform Sampling Schemes for RF Bandpass Sampling Receiver
    Bechir, Dadi Mohamed
    Ridha, Bouallegue
    PROCEEDINGS OF THE 2009 INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING SYSTEMS, 2009, : 13 - 17
  • [42] Low-Rank Approximation of Impedance Matrix Blocks Using Non-uniform Sampling Methods
    Brick, Yaniv
    Yilmaz, Ali E.
    2016 USNC-URSI RADIO SCIENCE MEETING (JOINT WITH AP-S SYMPOSIUM), 2016, : 47 - 48
  • [43] A new non-uniform adaptive-sampling successive approximation ADC for biomedical sparse signals
    Maryam Zaare
    Hassan Sepehrian
    Mohammad Maymandi-Nejad
    Analog Integrated Circuits and Signal Processing, 2013, 74 : 317 - 330
  • [44] A new non-uniform adaptive-sampling successive approximation ADC for biomedical sparse signals
    Zaare, Maryam
    Sepehrian, Hassan
    Maymandi-Nejad, Mohammad
    ANALOG INTEGRATED CIRCUITS AND SIGNAL PROCESSING, 2013, 74 (02) : 317 - 330
  • [45] A GLOBAL HIGH DIMENSIONAL METAMODELING APPROACH WITH THE ABILITY OF USING NON-UNIFORM SAMPLING
    Hajikolaei, Kambiz Haji
    Wang, G. Gary
    PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, 2014, VOL 2B, 2014,
  • [46] An Improvement of a Non Uniform Bound on Normal Approximation of Randomized Orthogonal Array Sampling Designs
    Rerkruthairat, N.
    Neammanee, K.
    COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2013, 42 (01) : 118 - 134
  • [47] Data Sampling and Processing: Uniform vs. Non-Uniform Schemes
    Beyrouthy, Taha
    Fesquet, Laurent
    Rolland, Robin
    PROCEEDINGS OF FIRST INTERNATIONAL CONFERENCE ON EVENT-BASED CONTROL, COMMUNICATION AND SIGNAL PROCESSING EBCCSP 2015, 2015,
  • [48] Non-Uniform Sampling and Reconstruction from Sampling Sets with Unknown Jitter
    Akram Aldroubi
    Casey Leonetti
    Sampling Theory in Signal and Image Processing, 2008, 7 (2): : 187 - 195
  • [49] Non-uniform Sampling Point Selection in OFDM Receiver with Fractional Sampling
    Nishimura, Haruki
    Inamori, Mamiko
    Sanada, Yukitoshi
    Ghavami, Mohammad
    2009 IEEE PACIFIC RIM CONFERENCE ON COMMUNICATIONS, COMPUTERS AND SIGNAL PROCESSING, VOLS 1 AND 2, 2009, : 837 - 842
  • [50] Secretary Problems with Non-Uniform Arrival Order
    Kesselheim, Thomas
    Kleinberg, Robert
    Niazadeh, Rad
    STOC'15: PROCEEDINGS OF THE 2015 ACM SYMPOSIUM ON THEORY OF COMPUTING, 2015, : 879 - 888
12345