Finding the maximum likelihood estimates ?

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Apurva Narayan
Apurva Narayan 2013-4-23
I need to find the MLE estimates. My code is as below. It seems to give me the correct mean but incorrect variance.
function obj = kmlepdf(x,y)
f1 = -1*50*log(2*pi*(y(2)));
f2 = ((y(2)));
f3 = ((x-y(1)).^2);
obj = (f1 + sum(0.5*(f3./f2))); % Normal Function
end
clear all;
load data;
y0 = [0.5 0.5];
lb = [0 0];
ub = [10 10];
% Assign Data to a new variable
x = data;
% Calling the Least Square Minimization
opts=optimset('DerivativeCheck','on','Display','off','TolX',1e-6,'TolFun',1e- 6,'Diagnostics','off','MaxIter',200);
[y, fval] = fmincon(@(y)kmlepdf(x,y),y0,[],[],[],[],lb,ub,[],opts)

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回答（1 个）

Tom Lane
Tom Lane 2013-4-24
I believe you want
f1 = 0.5*length(x)*log(2*pi*(y(2)));
You start with 1/sqrt(2*pi*sigma^2), then take logs so you get a minus sign, but you need to negate again to get the negative log likelihood that you can minimize.
Also try setting lb(2)=eps.

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