Suppose the data follow the model yi xii where xi 0 0 and

Suppose the data follow the model yi = xii where xi > 0, > 0, and the i are iid with density f(i) = ei.
(a) Obtain the MLE of .

(b) It turns out you are really interested in = 2 + 1. Obtain the MLE of .

(c) Suppose you want to test H0 : = 1. Give the likelihood ratio test statistics.

Solution

If the model is Yi=Xi+ei, then the MLE of ,=>^=+(X\'X)^-1X\'.