Tell me more ×
Cross Validated is a question and answer site for statisticians, data analysts, data miners and data visualization experts. It's 100% free, no registration required.
up vote -1 down vote favorite

If the minimum is not unique and the MLE is equal to zero over a range of functions, how can we find the minimum? I have read about golden section search algorithm or bisection algorithm, but I don't know if they would apply in this case or not? Is there any other better algorithm which is faster than these algorithms in R?

share|improve this question
3  
Uuuhh.. ? If the minimum is not unique then THE minimum does not exist. Do you mean there are several local minima ? What do you mean by "zero over a range of functions" ? Do you have an example of such a likelihood ? – Stéphane Laurent Jul 16 '12 at 7:05
When you say "the minimum is not unique" I hope you mean that there are multiple local minima but still a unique global minimum. In that situation, you could try starting your minimization algorithm from several different parts of the space to see where the "lowest" converged point is. In general, there is no silver bullet to handling optimization problems involving multi-modal functions but these kinds of informal procedures are useful. – Macro Jul 16 '12 at 14:29

1 Answer

up vote 3 down vote

I think you should look at the quasi-newton optimization through the function optim() function. You should also look at the packages and function listed under the optimization cran task view: http://cran.r-project.org/web/views/Optimization.html

Ideally, you should try a few different methods and see which produces the best results for your problem. If you have several local critical points, it's important to use different starting values. Selecting random starting values over the range of the function usually works well.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.