Deduce from the previous exercise that if the vector having components i,i lies in the column space of the model matrix X, then l3

Deduce from the previous exercise that if the vector having components ρi,i lies in the column space of the model matrix X, then l3 ≡

k3. More generally, prove that if the constant vector lies in the column space of X, then n

1/2 (l3 − k3) = Op (n

−1)

for large n under suitably mild limiting conditions on X. Hence, deduce that k3 is nearly optimal under normality.