88 lines
3.6 KiB
Matlab
88 lines
3.6 KiB
Matlab
function [abscissa,f] = kernel_density_estimate(data,number_of_grid_points,number_of_draws,bandwidth,kernel_function)
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% Estimates a continuous density.
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%
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% INPUTS
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% data [double] Vector (number_of_draws*1) of draws.
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% number_of_grid_points [integer] Scalar, number of points where the density is estimated.
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% This (positive) integer must be a power of two.
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% number_of_draws [integer] Scalar, number of draws.
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% bandwidth [double] Real positive scalar.
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% kernel_function [string] Name of the kernel function: 'gaussian', 'triweight',
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% 'uniform', 'triangle', 'epanechnikov', 'quartic',
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% 'triweight' and 'cosinus'
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%
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% OUTPUTS
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% abscissa [double] Vector (number_of_grid_points*1) of values on the abscissa axis.
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% f: [double] Vector (number_of_grid_points*1) of values on the ordinate axis,
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% (density estimates).
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%
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% SPECIAL REQUIREMENTS
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% none.
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%
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% REFERENCES
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% A kernel density estimator is used (see Silverman [1986], "Density estimation for statistics and data analysis")
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% The code is adapted from Anders Holtsberg's matlab toolbox (stixbox).
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%
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% Copyright © 2004-2017 Dynare Team
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%
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% This file is part of Dynare.
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%
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% Dynare is free software: you can redistribute it and/or modify
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% it under the terms of the GNU General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% Dynare is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU General Public License for more details.
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%
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% You should have received a copy of the GNU General Public License
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% along with Dynare. If not, see <https://www.gnu.org/licenses/>.
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if min(size(data))>1
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error('kernel_density_estimate:: data must be a one dimensional array.');
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else
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data = data(:);
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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)) > 1e-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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%% Kernel specification.
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if strcmpi(kernel_function,'gaussian')
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kernel = @(x) inv(sqrt(2*pi))*exp(-0.5*x.^2);
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elseif strcmpi(kernel_function,'uniform')
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kernel = @(x) 0.5*(abs(x) <= 1);
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elseif strcmpi(kernel_function,'triangle')
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kernel = @(x) (1-abs(x)).*(abs(x) <= 1);
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elseif strcmpi(kernel_function,'epanechnikov')
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kernel = @(x) 0.75*(1-x.^2).*(abs(x) <= 1);
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elseif strcmpi(kernel_function,'quartic')
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kernel = @(x) 0.9375*((1-x.^2).^2).*(abs(x) <= 1);
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elseif strcmpi(kernel_function,'triweight')
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kernel = @(x) 1.09375*((1-x.^2).^3).*(abs(x) <= 1);
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elseif strcmpi(kernel_function,'cosinus')
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kernel = @(x) (pi/4)*cos((pi/2)*x).*(abs(x) <= 1);
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end
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%% Non parametric estimation (Gaussian kernel should be used (FFT)).
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lower_bound = min(data) - (max(data)-min(data))/3;
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upper_bound = max(data) + (max(data)-min(data))/3;
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abscissa = linspace(lower_bound,upper_bound,number_of_grid_points)';
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inc = abscissa(2)-abscissa(1);
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xi = zeros(number_of_grid_points,1);
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xa = (data-lower_bound)/(upper_bound-lower_bound)*number_of_grid_points;
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for i = 1:number_of_draws
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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]'*inc;
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kk = kernel(xk/bandwidth);
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kk = kk / (sum(kk)*inc*number_of_draws);
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f = ifft(fft(fftshift(kk)).*fft([ xi ; zeros(number_of_grid_points,1) ]));
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f = real(f(1:number_of_grid_points)); |