
THREE DETAILED EXAMPLES 115
U = (U
1
,.. . ,U
n
)
>
and U
i
∼ t
ν
, independent, for i = 1, ... , n. For this location pa-
rameter problem, invariance considerations suggest the following decomposition:
X −T (X)1
n
= U −T (U )1
n
and T (X ) = θ + T (U),
where T (·) is the maximum likelihood estimator. Let V
T
= T (U) and V
H
= H(U ) =
U −T (U )1
n
. If h is the observed H(X), then it follows from the result of [8] that the
conditional distribution of V
T
, given V
H
= h, has a density
f
ν,h
(v
T
) = c(ν,h)
n
∏
i=1
ν + (v
T
+ h
i
)
2
−(ν+1)/2
,
where c(ν, h) is a normalizing constant that depends only on ν and h. If we write
F
ν,h
for the distribution function corresponding to the density ...