Let X D= Np(θ, Σ). Show that there exists a transformation Y = BX, such that Y D= Np(ξ, Ip) where ξ = (ξ1,ξ2,... ,ξp) and ξ1 = ³ θ ⊤Σ −1 θ ´1/2 while ξ2 = ... = ξp = 0. Let X D= Np(θ, Σ). and g(x) be...

Let X D= Np(θ, Σ). Show that there exists a transformation Y = BX, such that Y D= Np(ξ, Ip) where ξ = (ξ1,ξ2,... ,ξp) and ξ1 = ³ θ ⊤Σ −1 θ ´1/2 while ξ2 = ... = ξp = 0.

Let X D= Np(θ, Σ). and g(x) be a function of x, such that IEg(X) exists. Then g(x) → g ∗ (y) where y is defined as in Problem 8.7.1.