
EXAMPLES 135
and the baseline association (7.7) can be re-expressed as
kXk
2
= (ψ +V
1
)
2
+ kV
2:n
k
2
and
X −M
−1
V
kX −M
−1
V k
= ξ .
This is of the regular form (7.4), so the left-most equation above gives a marginal
IM for ψ. We make one more change of auxiliary variable, W = F
n,ψ
(ψ + V
1
)
2
+
kV
2:n
k
2
, where F
n,ψ
is the distribution function of a non-central chi-square with n
degrees of freedom and non-centrality parameter ψ
2
. The new marginal association
is kXk
2
= F
−1
n,ψ
(W ), with W ∼ Unif(0, 1), and the A-, P-, and C-steps can proceed
as usual. In particular, for the P-step, we can use the predictive random set S in
(4.8). However, the set Ψ
x
(w) = {ψ : kxk
2
= F
n