Question: Suppose p n b ! d N 0, v2 and set 2 and b b2. (a) Use the DeltaMethod to

Suppose p

n

¡bµ¡µ

¢

¡!

d N

¡

0, v2¢

and set ¯ Æ µ2 and b¯ Æ bµ2.

(a) Use the DeltaMethod to obtain an asymptotic distribution for p

n

¡ b¯¡¯

¢

.

(b) Now suppose µ Æ 0. Describe what happens to the asymptotic distribution fromthe previous part.

(c) Improve on the previous answer. Under the assumption µ Æ 0, find the asymptotic distribution for n b¯ Æ nbµ2.

(d) Comment on the differences between the answers in parts 1 and 3.

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