What is the analytical expression of the epanechnikov kernel used in kdensity?

Question

Samuel M 2024-11-18，11:51

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2166973-what-is-the-analytical-expression-of-the-epanechnikov-kernel-used-in-kdensity

I am using the kdensity function to obtain the density function of some data that is bounded at the top and bottom. As kernel I am using an epanechnikov kernel.

[pdf_kdensity,~,bwpdf] = ksdensity(data,x_values,'Support',[-0.1,(max(data)+0.1)],'BoundaryCorrection','reflection','Bandwidth','plug-in','Kernel','epanechnikov','Function','pdf')

Once kdensity adjusts the data and the optimal bandwidth value is obtained, I would like to build the function I have adjusted, for that I have built the following function:

function [f_epa]= epanechnikov_Kernel(data, h, L, U)
    % Parameters:
    % - data
    % - h: bandwidth
    % - L: lower bound
    % - U: uper bound
    %
       
    % Kernel  Epanechnikov
    K_epa = @(u) (abs(u) <= 1) .* (3/4) .* (1 - u.^2);
    
    
    f_epa = @(x) arrayfun(@(xi) (sum(K_epa((xi - data) / h)) + ...           
                                 sum(K_epa((xi - (2 * L - data)) / h)) + ...
                                 sum(K_epa((xi - (2 * U - data)) / h))) / (length(data) * h), x);
end

When I use this function, my results are not the same as what I get with kdensity.

f_epa= epanechnikov_Kernel(data, h, L, U)
mypdf=f_epa(data,bwpdf,-0.1,(max(data)+0.1))
figure()
hold on
plot(x_values,mypdf,"Color",'blue',LineWidth=1.5)
plot(x_values, pdf_kdensity,"Color",'red',LineWidth=1);
legend('kdensity epanechnikov','myfunction epanechnikov')
hold off

However, if I adjust the data with kdensity using a normal kernel and try to replicate those results with a function programmed by me, the results do match.

[pdf_kdensity_gauss,~,bwpdf_gauss] = ksdensity(data,x_values,'Support',[-0.1,(max(data)+0.1)],'BoundaryCorrection','reflection','Bandwidth','plug-in','Kernel','normal','Function','pdf')
function [f_gauss]= gauss_Kernel(data, h, L, U)
    % Parameters:
    % - data
    % - h: bandwidth
    % - L: lower bound
    % - U: uper bound
    
    % Kernel Gaussiano
    K_gauss = @(u) (1/sqrt(2*pi)) .* exp(-0.5 * u.^2);
    
    
    f_gauss = @(x) arrayfun(@(xi) (sum(K_gauss((xi - data) / h)) + ...           
                                    sum(K_gauss((xi - (2 * L - data)) / h)) + ...
                                   sum(K_gauss((xi - (2 * U - data)) / h))) / (length(data) * h), x);
end
f_gauss= gauss_Kernel(data, h, L, U)
mypdf_gauss=f_epa(data,bwpdf_gauss,-0.1,(max(data)+0.1))
figure()
hold on
plot(x_values,mypdf_gauss,"Color",'blue',LineWidth=1.5)
plot(x_values, pdf_kdensity_gauss,"Color",'red',LineWidth=1);
legend('kdensity epanechnikov','myfunction epanechnikov')
hold off

Therefore, I think that the differences between kdensity and my function when using the epanechnikov kernel are due to the fact that they use different expressions to fit the data.

In short, which expression does kdenstiy use for the epanechnikov kernel? I am using

Thank you very much

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

What is the analytical expression of the epanechnikov kernel used in kdensity?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

回答（0 个）

另请参阅

类别

标签

产品

Community Treasure Hunt

What is the analytical expression of the epanechnikov kernel used in kdensity?

0 个评论 显示 -2更早的评论隐藏 -2更早的评论

回答（0 个）

另请参阅

类别

标签

产品

Community Treasure Hunt

0 个评论
显示 -2更早的评论隐藏 -2更早的评论