I don't understand the solution at all. For me it seems that the largest observation =0.92 minimises the likelihood function. Could anybody explain that to me please?
They make you draw the graph to show that the L(theta) is a decreasing function from the largest value in the sample. It is not sensible to have a maximum likelihood larger than the largest sample value. The uniform disbn is a bit special with respect to parameter estimation.
But using the smaller observed values give an estimate that is not valid. Eg If we used 0.87 we'd have X~U(-0.87,0.87) but then the sample value 0.92 is not in this range! So the estimate is rubbish. See Example 10.5 in the notes.
