# Interpretation of Maximum likelihood estimation

I have a problem interpreting the result of performing maximum likelihood estimation.

The log likelihood function is:
$\sum^{n}_{i=1}\log\left( \phi\left( \frac{w-\mu}{\sigma}\right)\right) -\log(\sigma P(1)) +\log\left[ \frac{\left[ \Phi^{2}\left( \frac{w-\mu}{\sigma}\right)\right] }{2}-\delta \Phi\left( \frac{w-\mu}{\sigma}\right)+\left( \frac{a^{2}}{2} + b\right) \right].$

I get this output:

Is it possible to get some advice about how to interpret it?

• It would help if you told us more about the likelihood function that you are using and how mu, sigma, a and e appear in it. Commented Apr 12, 2014 at 20:03
• I edit the question adding the log likelihood function
– Lea
Commented Apr 12, 2014 at 20:19
• I see mu and sigma, but no a and e in the LLF, but there's is a delta and a strange P(1) term that you are not initializing. Commented Apr 12, 2014 at 20:37
• P(1) is some constant term
– Lea
Commented Apr 12, 2014 at 20:40

The output gives you output similar to what you'd see in a regression table - estimates and standard errors (which will probably be of primary interest) and p-values for a test of whether the coefficient differs from zero.

In large samples, you could use the asymptotic normality to construct approximate CIs for parameter estimates.

In most cases of MLE, a test of whether the coefficient differs from zero isn't a particularly interesting thing to test, but with the information given you could construct a test for any other specific value.

I am not sure there's any adequate basis for calling that a t-test, but it is asymptotically normal and its interpretation would be similar.