KERNELSTATS Return 2'nd order moment of kernel pdf as well as the integral of the squared kernel and integral of squared double derivative of kernel. CALL: [mu2, R, Rdd] = kernelstats(kernel) mu2 = 2'nd order moment, i.e.,int(x^2*kernel(x)) R = integral of squared kernel, i.e., int(kernel(x)^2) Rdd = integral of squared double derivative of kernel, i.e., int( (kernel''(x))^2 ). kernel = string identifying the kernel, i.e., one of: '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. Example [mu2,R]=kernelstats('triweight') See also mkernel
Biased Cross-Validation estimate of smoothing parameter. | |
Biased Cross-Validation smoothing parameter for 2D data. | |
Bootstrap cross-validation estimate of smoothing parameter. | |
L-stage Direct Plug-In estimate of smoothing parameter. | |
L-stage DPI estimate of smoothing parameter for 2D data | |
L-stage DPI estimate of smoothing parameter for 2D data | |
Normal Scale Estimate of Smoothing Parameter. | |
Smoothed cross-validation estimate of smoothing parameter. | |
2-Stage Solve the Equation estimate of smoothing parameter. | |
Scott-Tapia-Thompson estimate of smoothing parameter. |
001 function [mu2, R, Rdd] = kernelstats(kernel) 002 %KERNELSTATS Return 2'nd order moment of kernel pdf 003 % as well as the integral of the squared kernel 004 % and integral of squared double derivative of kernel. 005 % 006 % CALL: [mu2, R, Rdd] = kernelstats(kernel) 007 % 008 % mu2 = 2'nd order moment, i.e.,int(x^2*kernel(x)) 009 % R = integral of squared kernel, i.e., int(kernel(x)^2) 010 % Rdd = integral of squared double derivative of kernel, i.e., 011 % int( (kernel''(x))^2 ). 012 % kernel = string identifying the kernel, i.e., one of: 013 % 'epanechnikov' - Epanechnikov kernel. 014 % 'biweight' - Bi-weight kernel. 015 % 'triweight' - Tri-weight kernel. 016 % 'triangluar' - Triangular kernel. 017 % 'gaussian' - Gaussian kernel 018 % 'rectangular' - Rectanguler kernel. 019 % 'laplace' - Laplace kernel. 020 % 'logistic' - Logistic kernel. 021 % 022 % Note that only the first 4 letters of the kernel name is needed. 023 % 024 % Example 025 % [mu2,R]=kernelstats('triweight') 026 % 027 % See also mkernel 028 029 % Reference 030 % Wand,M.P. and Jones, M.C. (1995) 031 % 'Kernel smoothing' 032 % Chapman and Hall, pp 176. 033 034 %History 035 % by pab Dec2003 036 037 switch lower(kernel(1:4)) 038 case 'biwe', % Bi-weight kernel 039 mu2 = 1/7; 040 R = 5/7; 041 Rdd = 45/2; 042 case {'epan' 'epa1'}, % Epanechnikov kernel 043 mu2 = 1/5; 044 R = 3/5; 045 Rdd = inf; 046 case {'gaus','norm'}, % Gaussian kernel 047 mu2 = 1; 048 R = 1/(2*sqrt(pi)); 049 Rdd = 3/(8*sqrt(pi)); 050 case 'lapl', % Laplace 051 mu2 = 2; 052 R = 1/4; 053 Rdd = inf; 054 case 'logi', % Logistic 055 mu2 = pi^2/3; 056 R=1/6; 057 Rdd = 1/42; 058 case {'rect','unif'}, % Rectangular 059 mu2 = 1/3; 060 R = 1/2; 061 Rdd = inf; 062 case 'tria', % Triangular 063 mu2 = 1/6; 064 R = 2/3; 065 Rdd = inf; 066 case 'triw', % Triweight 067 mu2 = 1/9; 068 R = 350/429; 069 Rdd = inf; 070 otherwise 071 error('Unknown kernel.') 072 end;
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