132
4 ( n ^ 2 )
( n-1 )
*(4 lc )
1
4nc P(4,3 c)
(n-1) i
is a consistent estimator for
4Cov(f(X1.- X2i+ Xlj- X2j>- aikbikl i-ij-M
and that
2(nc _1) A ( 5 2 c ) 2nl ^(5,3c)
(n-1) + (n-1)
is a consistent estimator for
2Cov(l-2y., a..b..|.e(2,3)},
1 J ij ij 1 3 J
the proof will be complete. Recalling that
nl p nc P
* X^ and -v X^, we observe that asymptotically,
the coefficient in front of each £ terra is the probability
necessary to uncondition the term so that within each
estimator the terras can be combined appropriately. (See
page 118 for a similar argument.) Also, since each
estimator is a U-statistic, it follows that each is
consistently estimating the appropriate covariance term and
the proof of Lemma 4.5.2 follows