97
Thus ,
TE
n
1
* / \
TE
c
Tc i
Uj)1^ (3 )l/2 (U1>ni- V2 )
*1/2 ojVa (U2 ni- V2 )
<"c)1/2 <3,nc>
(nc)V2 (3)V2 (U4>nc- V2 )
op(l)
p(l))
op(I)
and therefore, if we can show the right hand side has the
appropriate distribution, the proof will be complete.
First, it will be shown that
U =
where
1/2
"/2 <"2,ni- \ >
1,1/2
c
> N(0,i )
- T u
"/2 (D4,nc- V2 )
/, (a,b) (a,b) v 1
= ((a )) and a = i
2
I
i = l
rU)r(b)
( a b )
lim () and £ is the covariance term described in
n + n i
Theorem 3.6.9 of Randles and Wolfe ( 1979 pg 107).
Note, conditional on N^=n^ and Nc=nc, the problem can be
considered as a two sample problem. By Theorem 3.6.9
(Randles and Wolfe, 1979, pg. 107) it follows that
*