128
( i e ,
The first estimation problem has already been taken care of
in Section 2.4. The method of solving the second estimation
k
problem is similar to that used for estimating 12P That
is, the exact covariance between TE and CD is derived
n 1 >nc
and the sample quantities are then used in its
calculation. Lemma 4.5.2 will present this estimator and
argue that this is a consistent estimator for the asymptotic
covariance. This estimator will be actually in the form of
two estimators; one which is estimating the covariance of
TE and CD and the other which is estimating the covariance
nl
of TEn and CD. This is equivalent to estimating the
c
quantities
and
C o v [ ( 1 2Yj), aijbj | 6jG(2,3)]
First though, we describe some notation which will be
needed. Let h^3^(X^) and h^^^(X^, X^ ) be defined as
before. In addition, define
h<5)(?j) *
= h(3)(Xi)h(lc)(Xi,Xj)
+ h(3)(X;j)h(lc)(Xi,X:j) ,