Do M-estimators and L-estimators overlap? In my self-study, I have read the wikipedia entries and some books in regards to M-estimators and L-estimators.
I understand that M-estimators are so called "M" because they "Maximize" the likelihood function, and/or functions of the data itself. I also understand that L-estimators are so called because they use "Linear" combinations of order-statistics of the data.
It seems to me though that there are overlaps between M-estimators and L-estimators, is this not correct? (For example, the mean seems to me that it can be derived as an M-estimator, or as an L-estimator). 
Put another way, if we were to draw a Venn Diagram of all M and L estimators, how much would they overlap with each other, if at all? 
Edit:
Thanks to the feedback, I understand that such a Venn Diagram might have infinite elements. What I would like however, is very rough percentages of overlap, based on ones' experience, since I know that this experience is far greater than mine! I am just after a rough estimate based on what experts and practitioners in the field have seen and come across. 
Thank you.
 A: There are certainly M-estimators that are L-estimators. 
An example: the sample median is both an M-estimator and an L-estimator. It's maximum likelihood for the location parameter of a Laplace (double exponential).
The sample midrange is arguably both an M-estimator and an L-estimator, too. I believe it's the maximum likelihood estimator for the center ($\theta$) of a uniform on $(\theta-\phi/2,\theta+\phi/2)$.

the mean seems to me that it can be derived as an M-estimator, or as an L-estimator

Yes, that's another example. 

Put another way, if we were to draw a Venn Diagram of all M and L estimators, how much would they overlap with each other, if at all? 

I don't know that this is an especially useful way to look at it; my guess is that the number of estimators in the intersection could well be infinite, but may well be a vanishingly-small fraction of the union. But I think it would be very difficult to actually do this calculation, and I believe most of the estimators contained in it would not be interesting for any real-world application.
What might be of more relevance is the proportion of estimators in wide use (amongst those that are M-, or perhaps L-), that are both. But this then gets into issues of personal opinion about definitions and difficulties of estimation (what's 'wide'? how would we measure this?)
I'd think there's probably quite a few that are both, but as a proportion of say all M-estimators that get used/discussed, probably not that large a fraction.
A: Here is a Venn Diagram showing the overlap between M- and L-estimators.

