66
(j)
1 if Y,.. is censored
(j )
0 otherwise
in the fact that
2 n
/, \ = y y i(x..> y,. )
(1) lilj-l ^
X
= 2n + 1 (rank of Y^^ in (Y(i)>^(2)> ' >Y(2n)^
In addition, S(t) can be expressed as
S(t) =
1
0
t < min Y , : I, =
1 (i) (i)
1}
t > ma x Y x : I/.N
1 (i) (i )
= 1
n
2n j
X(j)
* ^2n j + 1
V (j)
otherwise
Thus, S(t) is a symmetric function with respect to the
sample observations and therefore M, being a function of
S(t), is also. Cl
Lemma 3.3
. 2 : Conditional on n^ Tn has the same null
distribution as the Wilcoxon signed rank statistic
Proof :
Let V = {Tj, 'P 2 where = and
R = R, R R I with R. =
1 1 2 n ^ i
Let V be any arbitrary element of
P = i V is a 1 x n, vecto
1 -o -o 1
absolute rank of Z ^