Difference between restricted and unrestricted parameter space in MLE

I searched on the internet but I could not find any clues about my question. Can anyone just simply tell what is the difference between restricted and unrestricted parameter space in MLE?

I have used bimodalitytest package in R, the function bimodality.test which performs the likelihood ratio test for bimodality.

It's description is:

"This function performs the likelihood ratio test for a given dataset. It tests the null hypothesis, whether a two components normal mixture is bimodal. Therefore it calculates the maximum likelihood estimators for the restricted and non restricted parameter space and returns for example the likelihoodratio and the p-value."

And I know the next question depends on the purpose of research and other points, but let me also ask it:

Which one do you suggest for MLE? restricted or non restricted parameter space? On which basis should I decide on using them?

• Are you referring to estimates for situations where data collection is incomplete in certain or variable regions of the range of data, so called truncated or censored data? – DWin Feb 21 '15 at 18:53
• ok, I revise my question with more information. – Ehsan Feb 21 '15 at 19:19
• I think with revised one, now it's clear what I'm looking for. Thank you for your comment – Ehsan Feb 21 '15 at 19:23

 f(x;θ1,θ2,p) = pf(x;θ1) + (1 − p)f(x;θ2), where