calculating Kernel density for each column

Hi

Please how do I need a short code that will calculate the KDE of each column in the R.length data below

the KDE is given as = I/n*h sum ( K * (( v - i )/h) which is computed for each column

where h = 1.06 * variance * (n^(-0.2)) for each colum

n is the number of each column

i = first, second, third, fourth, fifth, sixth number of each column

v =pv is given as 3, 4, 5, 6 for each column

Thanks in advance

jonathan

R = [ 0.6164 3.4161 0.9950 3.4117;

3.1654 0.4123 4.2391 1.0198;

0.5745 3.0364 1.3191 3.1129;

2.9883 0.7348 3.8730 0.4123;

0.9381 3.3749 2.0421 3.5014;

2.1817 1.0630 3.0643 0.9487];

[Rik]

What have you tried so far? Have a read here and here. It will greatly improve your chances of getting an answer.

[David Wilson]

Would ksdensity work? (From stats toolbox)

[Rik]

'Answer' by Jonathan Etumusei moved to comment and formatted:

This is what I have done so far and the answers are below

thanks

n = 6;
K = 3;
h1 = 1.06 * var(Z(:,1)) * (n ^ 0.2);
h2 = 1.06 * var(Z(:,2)) * (n ^ 0.2);
h3 = 1.06 * var(Z(:,3)) * (n ^ 0.2);
h4 = 1.06 * var(Z(:,4)) * (n ^ 0.2);
z1 = 1/ (n * h1);
z2 = 1/ (n * h2);
z3 = 1/ (n * h3);
z4 = 1/ (n * h4);
Ec11 = (K * (v1 - Z(1,1))/h1) ;
Ec12 = (K * (v1 - Z(2,1))/h1) ;
Ec13 = (K * (v1 - Z(3,1))/h1) ;
Ec14 = (K * (v1 - Z(4,1))/h1) ;
Ec15 = (K * (v1 - Z(5,1))/h1) ;
Ec16 = (K * (v1 - Z(6,1))/h1) ;
e1 = [Ec11; Ec12; Ec13; Ec14; Ec15; Ec16];
e1 = sum (e1);
Ec21 =  K * (v2 - Z(1,2)/h2);
Ec22 = (K * (v2 - Z(2,2))/h2) ;
Ec23 = (K * (v2 - Z(3,2))/h2) ;
Ec24 = (K * (v2 - Z(4,2))/h2) ;
Ec25 = (K * (v2 - Z(4,2))/h2) ;
Ec26 = (K * (v2 - Z(4,2))/h2) ;
e2 = [ Ec21; Ec22; Ec23; Ec24; Ec25; Ec26];
e2 = sum (e2);
Ec31 =  K * (v3 -  Z(1,3)/h3);
Ec32 = (K * (v3 -  Z(2,3))/h3) ;
Ec33 = (K * (v3 -  Z(3,3))/h3) ;
Ec34 = (K * (v3 -  Z(4,3))/h3) ;
Ec35 = (K * (v3 -  Z(5,3))/h3) ;
Ec36 = (K * (v3 -  Z(6,3))/h3) ;
e3 = [Ec31; Ec32; Ec33; Ec34; Ec35; Ec36];
e3 = sum (e3);
Ec41 =  K * (v4 - Z(1,4)/h4);
Ec42 = (K * (v4 - Z(2,4))/h4) ;
Ec43 = (K * (v4 - Z(3,4))/h4) ;
Ec44 = (K * (v4 - Z(4,4))/h4) ;
Ec45 = (K * (v4 - Z(5,4))/h4) ;
Ec46 = (K * (v4 - Z(6,4))/h4) ;
e4 = [Ec41; Ec42; Ec43; Ec44; Ec45; Ec46];
e4 = sum(e4);
k = e1;
l = e2;
m = e3;
b = e4;
% the kernal density estimation
KDE1 = k * z1;
KDE2 = l * z2;
KDE3 = m * z3;
KDE4 = b * z4;

answer

   -0.4881
   -0.1668
   -0.7734
   -0.3972

[Rik]

Instead of using numbered variables, why don't you process the columns in a loop?

[Tino]

Yes but how do I do that ?

Answer 1

[Rik]

I am assuming the v values are the same as the column index, and that you made a mistake with the code for the second column.

Z =  [ 0.6164    3.4161    0.9950    3.4117;
    3.1654    0.4123    4.2391    1.0198;
    0.5745    3.0364    1.3191    3.1129;
    2.9883    0.7348    3.8730    0.4123;
    0.9381    3.3749    2.0421    3.5014;
    2.1817    1.0630    3.0643    0.9487];

n = 6;
K = 3;
z=zeros(1,size(Z,2));e=zeros(size(z));
for col=1:size(Z,2)
    v=col;%is this what you mean?
    h = 1.06 * var(Z(:,col)) * (n ^ 0.2);
    z(col) = 1/ (n * h);
    E   = K * (v - Z(:,col))/h;
    if col~=1
        %did you mean for this to be different?
        E(1)= K * (v - Z(1,col)/h);
    end
    e(col) = sum(E) ;
end
% the kernal density estimation
KDE = e .* z;

[Tino]

Hi Rik

The v values are numbers obtained from a different computation below

strangeness1 = 0.25541

strangeness2 = 4.4465

strangeness3 = 0.38976

strangeness4 = 4.2112

using Si = [strangeness1,strangeness2, strangeness3, strangeness4];

% find the v-values

fnP=@(a,i)(sum(a(i)>a(1:i))+0.5*sum(a(i)==a(1:i)))/i;

Thanks in advance

Regards

Jonathan

[Rik]

Well, you know the inputs, you have working code, you should be able to integrate the calculation in my code. What issues are you having with that integration?