Take the Gammamodel f (x j ,) () x1ex , x 0. Assume

Take the Gammamodel f (x j ®,¯) Æ

¯®

¡(®)

x®¡1e¡¯x , x È 0.

Assume ¯ is known, so the only parameter to estimate is ®. Let g (®) Æ log¡(®). Write your answers in terms of the derivatives g 0(®) and g 00(®). (You need not get the closed formsolution for these derivatives.)

(a) Calculate the information for ®.

(b) Using the general formula for the asymptotic distribution of the MLE to find the asymptotic distribution of p

n(b®

¡®) where b®

is the MLE.

(c) Letting V denote the asymptotic variance from part (b), propose an estimator b V for V .