Estimation of Loss Distribution Parameters.

#1
At a "loss" with this one!

A statistician is trying to decide on the value of an unknown parameter ϴ, where ϴ is the maximum claim that can occur for a line of business whose claims are uniformly distributed on the interval (0, ϴ). In making the decision, the statistician randomly selects a single loss from the line of business, which takes the value x, and estimates ϴ as ϴ*=kx where k is a constant. The statistician is using a quadratic loss function: that is to say the loss incurred based on their decision is proportional to the squared distance between the true value ϴ and their estimate ϴ*. Find the form of their estimate ϴ* based on the sample outcome x in order to minimize the expected risk.
 

CowboyBear

Super Moderator
#2
Sorry for the delay in approving your post - it was caught in our spam filter for some reason. Approved now. Do please describe for us what you've done so far to figure out the problem, since this does seem like homework question(?)