Maximum of the log likelyhood function

[rjasg]

I am trying to estimate 3 parameters of a certain probability density function by maximization of the log likelyhood function . The problem is that I foun out that the maximum ML value is not attained when parameters assume their true value. I've never encountered this problem. Can you help me out?
Thank you so much,
Rui Gonçalves

 

[Dason]

Define what you mean by "true value"

 

[rjasg]

Thanks for your response and interest in helping out.
The true values are the ones used in the simulation and are those I am trying to estimate for testing. What I noticed is that for values close but not equal to the true ones the ML function has higher values. The difference is small so it can be a numerical problem but nevertheless it poses a problem in the estimation.

 

[Dason]

Maximum likelihood estimation is an estimation method. As with pretty much all parameter estimation methods one would never expect to perfectly estimate the parameter. There is always variation in the data.

 

[rjasg]

Maximum likelihood estimation is an estimation method. As with pretty much all parameter estimation methods one would never expect to perfectly estimate the parameter. There is always variation in the data.

I completely agree. Variation in data causes it. I will study estimation statistics on groups rather than point estimation.
Thanks Dason for the help.

 

[Dason]

I'm not sure what you mean by that but good luck I guess