almost uniform but far from straightforward

A question on X validated about a [not exactly trivial] maximum likelihood for a triangular function led me to a fascinating case, as exposed by Olver in 1972 in The American Statistician. When considering an asymmetric triangle distribution on (0,þ), þ being fixed, the MLE for the location of the tip of the triangle is necessarily one of the observations [which was not the case in the original question on X validated ]. And not in an order statistic of rank j that does not stand in the j-th uniform partition of (0,þ). Furthermore there are opportunities for observing several global modes… In the X validated case of the symmetric triangular distribution over (0,θ), with ½θ as tip of the triangle, I could not figure an alternative to the pedestrian solution of looking separately at each of the (n+1) intervals where θ can stand and returning the associated maximum on that interval. Definitely a good (counter-)example about (in)sufficiency for class or exam!

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: