Why is my code not working? I'm supposed to determine the mean of a biased and unbiased sample variance and plot but it's not working

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Kevin Nelson 2022-10-4

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https://ww2.mathworks.cn/matlabcentral/answers/1817645-why-is-my-code-not-working-i-m-supposed-to-determine-the-mean-of-a-biased-and-unbiased-sample-varia

回答： Image Analyst 2022-10-4

%% 1. Sample variance bias
Nd1 = [5, 10, 50, 100, 500, 1000];
trials2 = 100; 
sigma = 4;
samplevar = zeros(length(Nd1),trials2);
samplevarbias = zeros(length(Nd1),trials2);
for i=1:length(Nd1)
    uncorrected = (1/Nd1)*(sum(4^2 * 0^2));
    corrected = (1/Nd1 - 1)*(sum((4-0)^2));
end
% Compute mean of the two estimators.
% You may use matlab's mean function to compute the mean, but be careful to
% specify which dimension of the matrices you want to compute the mean
% over!
meansvar = mean(corrected);   % enter code
meansvarbias = mean(uncorrected); % enter code
% Plot figure. You do not need to modify this section.
figure; plot(Nd1,meansvar-sigma^2,'bo-','LineWidth',5)
hold on; plot(Nd1,meansvarbias-sigma^2,'rs-','LineWidth',5)
xlabel('$N_D$','Interpreter','latex','fontsize',20)
ylabel('Bias','Interpreter','latex','fontsize',20)
title('Bias of variance estimators','Interpreter','latex','fontsize',20)

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Answer 1

Image Analyst 2022-10-4

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https://ww2.mathworks.cn/matlabcentral/answers/1817645-why-is-my-code-not-working-i-m-supposed-to-determine-the-mean-of-a-biased-and-unbiased-sample-varia#answer_1066815

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I think you need an inner loop with Nd iterations. Here, start with this (still broken) code and see if you can figure it out:

%% 1. Sample variance bias
Nd1 = [5, 10, 50, 100, 500, 1000];
trials2 = 100;
sigma = 4;
samplevar = zeros(length(Nd1),trials2);
samplevarbias = zeros(length(Nd1),trials2);
for i=1:length(Nd1)
    thisN = Nd1(i);
    fprintf('Running with i = %d.  Will now do %d iterations.\n', thisN, thisN);
    % So the simulation with this number of iterations.
    for k = 1 : thisN
        uncorrected = (1/thisN)*(sum(4^2 * 0^2));  % Not sure about these!
        corrected = (1/thisN - 1)*(sum((4-0)^2));
    end
end
% Compute mean of the two estimators.
% You may use matlab's mean function to compute the mean, but be careful to
% specify which dimension of the matrices you want to compute the mean
% over!
meansvar = mean(corrected);   % enter code
meansvarbias = mean(uncorrected); % enter code
% Plot figure. You do not need to modify this section.
figure; plot(Nd1,meansvar-sigma^2,'bo-','LineWidth',5)
hold on; plot(Nd1,meansvarbias-sigma^2,'rs-','LineWidth',5)
xlabel('$N_D$','Interpreter','latex','fontsize',20)
ylabel('Bias','Interpreter','latex','fontsize',20)
title('Bias of variance estimators','Interpreter','latex','fontsize',20)
fprintf('Done!\n')