quasi maximum likelihood: parameter estimation issue

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bing xu
bing xu 2018-2-2
评论： bing xu 2018-2-3
Hi there. thanks for reading first. I got this problem stuck here for few days now, even it seems simple.but.... here is the problem:
I want to use mle function to estimate three parameters(u,phi,syst_sigma) in a customized PDF function. here is the code:
y=[-6.8949 -6.9075 -6.8989 -6.7401 -6.9062];
syms u phi syst_sigma
assume(phi>-1&phi<1);
mi=-1.2704;
measur_sigma=pi^2/2;
h(1)=0;
p(1)=1-phi^2/syst_sigma^2;
t=5;
for t=1:t
h=0.03+phi*h;
v=y(t)-(h+mi);
k=phi.*p/(p+measur_sigma^2);
h=h+k.*v;
p=(phi.*p/(phi-k))+syst_sigma^2;
l=((y(t)-u)^2/p)
P=sum(p)
l=sum((y(t)-u)^2/p)
end
%do the parameter estimation
pdf=@(y,u,phi,syst_sigma) -5/2*log(2*pi)-0.5.*P-0.5.*l;
phat=mle(y(1:end),'pdf',pdf,'start',[0,0.95,0.0]);
t will predefined to a number.I had run the section above '%do the parameter estimation' and it was fine. But after that, it keep come out a lot different error messages. So I come here to see if anyone can help to give some advices. Any comments would be appreciated. Thank you all .
  2 个评论
bing xu
bing xu 2018-2-3
Thank you Matt. I re-edit my question.I added t value and few y data on it as well.

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Matt J
Matt J 2018-2-3
编辑：Matt J 2018-2-3
%do the parameter estimation
nonsym=matlabFunction(-5/2*log(2*pi)-0.5.*P-0.5.*l);
logpdf=@(y,u,phi,syst_sigma) nonsym(phi,syst_sigma,u);
phat=mle(y(1:end),'logpdf',logpdf,'start',[0,0.95,1],'OptimFun','fmincon');
  1 个评论
bing xu
bing xu 2018-2-3
Matt Thank you so much. This really helps me a lot and your code works very well. I thought my code should modified by varargin and varargout but yours seems smarter.

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