Parzen Window Estimation example Old Kiwi - Rhea

PLEASE HELP FIX MATLAB CODE

I have tried replicating the results of figure 4.5 on page 169 of DHS. It shows Parzen-window estimates of a univariate gaussian density using different window widths and number of samples.

Here's the figure that I got from my MATLAB code. As you can see, my results do not match well with the figure of the book....especially for n=10, 100, 10000. I tried looking at the code for considerable amount of time but could not figure out what is wrong.

Here's the MATLAB code. It will be great if somebody can take a look at the code and try to match the results with the book.::

% This code replicates the results of figure 4.5 on page 169 of DHS
 
close all; clear;
 
h1 = [1 0.6 0.15];  % this parameter controls the window width h_n
n = [1 10 100 1e4]; % total number of samples
d = 1;  % number of dimensions
 
x = [-2:0.1:2]; % data points at which density will be estimated using parzen window method
len_x = length(x);
 
figure; hold on;
 
for row = 1:length(n)
  for col = 1:length(h1)
 
    disp(['n = ' num2str(n(row)) '    h1 = ' num2str(h1(col))]);
 
    hn = h1(col)/sqrt(n(row));  % look on page 168, DHS: h_n = h_1 / sqrt(n)
    Vn = hn^d;
 
    samples = random('normal',0,1,n(row),1);
 
    prob_estimate = zeros(1,len_x);
 
    for i = 1:len_x
      sum1=0;
      for j = 1:n(row)
        sum1 = sum1 + (1/sqrt(2*pi))*exp(-0.5*((x(i)-samples(j))/hn)^2)/hn;
      end
      prob_estimate(i) = sum1/n(row);
    end
 
    subplot(length(n), length(h1), (row-1)*length(h1)+col); plot(x,prob_estimate);
  end
end

Parzen Window Estimation example Old Kiwi - Rhea

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