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
Normal Scale Estimate of Smoothing Parameter. |
Biased Cross-Validation estimate of smoothing parameter. | |
Bootstrap cross-validation estimate of smoothing parameter. | |
Least Squares Cross-Validation estimate of smoothing parameter | |
Smoothed cross-validation estimate of smoothing parameter. |
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;
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