55 lines
2.1 KiB
Matlab
55 lines
2.1 KiB
Matlab
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function [abscissa,f] = kernel_density_estimate(data,number_of_grid_points,bandwidth,kernel_function)
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%% This function aims at estimating a continuous density. A kernel density
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%% estimator is used (see Silverman [1986]).
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%%
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%% * Silverman [1986], "Density estimation for statistics and data analysis".
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%%
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%% The code is adapted from Anders Holtsberg's matlab toolbox (stixbox).
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%%
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%% stephane.adjemian@cepremap.cnrs.fr [07/16/2004].
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if size(data,2) > 1 & size(data,1) == 1
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data = transpose(data);
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elseif size(data,2)>1 & size(data,1)>1
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error('kernel_density_estimate :: data must be a one dimensional array.');
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end
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test = log(number_of_grid_points)/log(2);
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if (abs(test-round(test)) > 10^(-12))
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error('kernel_density_estimate :: The number of grid points must be a power of 2.');
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end
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n = size(data,1);
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%% KERNEL SPECIFICATION...
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if strcmpi(kernel_function,'gaussian')
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k = inline('inv(sqrt(2*pi))*exp(-0.5*x.^2)');
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elseif strcmpi(kernel_function,'uniform')
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k = inline('0.5*(abs(x) <= 1)');
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elseif strcmpi(kernel_function,'triangle')
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k = inline('(1-abs(x)).*(abs(x) <= 1)');
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elseif strcmpi(kernel_function,'epanechnikov')
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k = inline('0.75*(1-x.^2).*(abs(x) <= 1)');
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elseif strcmpi(kernel_function,'quartic')
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k = inline('0.9375*((1-x.^2).^2).*(abs(x) <= 1)');
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elseif strcmpi(kernel_function,'triweight')
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k = inline('1.09375*((1-x.^2).^3).*(abs(x) <= 1)');
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elseif strcmpi(kernel_function,'cosinus')
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k = inline('(pi/4)*cos((pi/2)*x).*(abs(x) <= 1)');
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end
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%% COMPUTE DENSITY ESTIMATE... Gaussian kernel should be used (FFT).
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a = min(data) - (max(data)-min(data))/3;
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b = max(data) + (max(data)-min(data))/3;
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abscissa = linspace(a,b,number_of_grid_points)';
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d = abscissa(2)-abscissa(1);
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xi = zeros(number_of_grid_points,1);
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xa = (data-a)/(b-a)*number_of_grid_points;
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for i = 1:n;
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indx = floor(xa(i));
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temp = xa(i)-indx;
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xi(indx+[1 2]) = xi(indx+[1 2]) + [1-temp,temp]';
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end;
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xk = [-number_of_grid_points:number_of_grid_points-1]'*d;
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kk = k(xk/bandwidth);
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kk = kk / (sum(kk)*d*n);
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f = ifft(fft(fftshift(kk)).*fft([xi ;zeros(size(xi))]));
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f = real(f(1:number_of_grid_points));
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