Suppose X and Y are independent, with X distributed as P and Y as P , as

Suppose X and Y are independent, with X distributed as Pθ and Y as P¯

θ, as θ varies in a common index set . Assume the families {Pθ} and {P¯

θ} are q.m.d. with Fisher Information matrices IX (θ) and IY (θ), respectively. Show that the model based on the joint data (X, Y ) is q.m.d. and its Fisher Information matrix is given by IX (θ) + IY (θ).