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hos

PURPOSE ^

Oversmoothing Parameter.

SYNOPSIS ^

h=hos(A,kernel)

DESCRIPTION ^

 HOS Oversmoothing Parameter. 
  
  CALL:  h = hos(data,kernel) 
  
    h      = one dimensional maximum smoothing value for smoothing parameter 
             given the data and kernel.  size 1 x D 
    data   = data matrix, size N x D (D = # dimensions ) 
    kernel = 'epanechnikov'  - Epanechnikov kernel. 
             'biweight'      - Bi-weight kernel. 
             'triweight'     - Tri-weight kernel.   
             'triangluar'    - Triangular kernel. 
             'gaussian'      - Gaussian kernel 
             'rectangular'   - Rectanguler kernel.  
             'laplace'       - Laplace kernel. 
             'logistic'      - Logistic kernel. 
    
   Note that only the first 4 letters of the kernel name is needed. 
   
  The oversmoothing or maximal smoothing principle relies on the fact 
  that there is a simple upper bound for the AMISE-optimal bandwidth for 
  estimation of densities with a fixed value of a particular scale 
  measure. While HOS will give too large bandwidth for optimal estimation  
  of a general density it provides an excellent starting point for 
  subjective choice of bandwidth. A sensible strategy is to plot an 
  estimate with bandwidth HOS and then sucessively look at plots based on  
  convenient fractions of HOS to see what features are present in the 
  data for various amount of smoothing. The relation to HNS is given by: 
   
            HOS = HNS/0.93 
  
   Example:  
   data = wnormrnd(0, 1,20,1) 
   h = hos(data,'epan'); 
    
  See also  hste, hbcv, hboot, hldpi, hlscv, hscv, hstt, kde, kdefun

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

001 function h=hos(A,kernel) 
002 %HOS Oversmoothing Parameter. 
003 % 
004 % CALL:  h = hos(data,kernel) 
005 % 
006 %   h      = one dimensional maximum smoothing value for smoothing parameter 
007 %            given the data and kernel.  size 1 x D 
008 %   data   = data matrix, size N x D (D = # dimensions ) 
009 %   kernel = 'epanechnikov'  - Epanechnikov kernel. 
010 %            'biweight'      - Bi-weight kernel. 
011 %            'triweight'     - Tri-weight kernel.   
012 %            'triangluar'    - Triangular kernel. 
013 %            'gaussian'      - Gaussian kernel 
014 %            'rectangular'   - Rectanguler kernel.  
015 %            'laplace'       - Laplace kernel. 
016 %            'logistic'      - Logistic kernel. 
017 %   
018 %  Note that only the first 4 letters of the kernel name is needed. 
019 %  
020 % The oversmoothing or maximal smoothing principle relies on the fact 
021 % that there is a simple upper bound for the AMISE-optimal bandwidth for 
022 % estimation of densities with a fixed value of a particular scale 
023 % measure. While HOS will give too large bandwidth for optimal estimation  
024 % of a general density it provides an excellent starting point for 
025 % subjective choice of bandwidth. A sensible strategy is to plot an 
026 % estimate with bandwidth HOS and then sucessively look at plots based on  
027 % convenient fractions of HOS to see what features are present in the 
028 % data for various amount of smoothing. The relation to HNS is given by: 
029 %  
030 %           HOS = HNS/0.93 
031 % 
032 %  Example:  
033 %  data = wnormrnd(0, 1,20,1) 
034 %  h = hos(data,'epan'); 
035 %   
036 % See also  hste, hbcv, hboot, hldpi, hlscv, hscv, hstt, kde, kdefun 
037  
038 % Reference:   
039 %  B. W. Silverman (1986)  
040 % 'Density estimation for statistics and data analysis'   
041 %  Chapman and Hall, pp 43-48  
042  
043 %  Wand,M.P. and Jones, M.C. (1986)  
044 % 'Kernel smoothing' 
045 %  Chapman and Hall, pp 60--63 
046  
047  
048 %Tested on: matlab 5.3 
049 % History: 
050 % revised pab feb2005 
051 % -updated example + see also line   
052 % revised pab 21.09.99 
053 %  
054 % updated string comparisons 
055 % from kdetools 
056  
057 h=hns(A,kernel)/0.93;

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

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