# Question on maximum likelihood

1. Sep 29, 2007

### Simfish

http://en.wikipedia.org/wiki/Maximum_likelihood

What exactly does the "arg" here mean? It seems to be an unnecessary - the max L(\theta) seems to be sufficient enough. Or am I missing something?
$$\widehat{\theta} = \underset{\theta}{\operatorname{arg\ max}}\ \mathcal{L}(\theta).$$

2. Sep 29, 2007

### EnumaElish

arg is needed because the left-hand side is the argument of L.

One can write $$L(\widehat{\theta}) = \underset{\theta}\max\ {L(\theta)}.$$.

Or one can write $$\widehat{\theta} = \underset{\theta}{\operatorname{arg\ max}}\ {L}(\theta).$$