# [R] Help: Maximum likelihood estimation

roach roachyang at gmail.com
Fri Oct 22 04:23:48 CEST 2010

```I was trying to reproduce a result in a published journal, and I have come
across some difficulties.
I have the following equation, which is two equations combined together.
http://r.789695.n4.nabble.com/file/n3006584/Screenshot.png
where
http://r.789695.n4.nabble.com/file/n3006584/Screenshot-1.png
http://r.789695.n4.nabble.com/file/n3006584/Screenshot-2.png
http://r.789695.n4.nabble.com/file/n3006584/Screenshot-3.png
I[t] is unknown, but have the following distribution
http://r.789695.n4.nabble.com/file/n3006584/Screenshot-4.png
hence, the probability density function is
http://r.789695.n4.nabble.com/file/n3006584/Screenshot-5.png
and the likelihood function is
http://r.789695.n4.nabble.com/file/n3006584/Screenshot-6.png
It used Kiefer's E-M algorithm to estimate the problem. To simplify, first
assume lamda is known. I multiply the matrix in the probability density
function, and write it in a non-matrix form, and use the function optim() to
estimate the maximum. but I got non-sensible estimates of the parameters,
and got 39 warnings. the inverse of sigma is negative, and the warnings says
that in log(det(sigma)): NaNs produced.
What did I do wrong? Can anybody give me a hint?
--
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