594
Appendix B
(D2)
For generalized least squares estimation (GLS), , and are obtained by
taking f to be:
(D3)
For asymptotically distribution-free estimation (ADF), , and are obtained
by taking f to be:
(D4)
where the elements of are given by Browne (1984, Equations 3.1–3.4):
() () () ()
()
() () () ()
()
() () () ()
()
() () ()
()
() () () ()
()
() () ()
()
.logtrlog gggggggggg
gggg
KL
gggg
KL
gggg
ML
p
fff
μμ
μμ
−Σ
′
−+−−Σ+Σ=
−Σ=Σ
−− xxSS
S,x;S,xS,x;,S,x;,
11
CGLS
FGLS
() ()
()
() () ()
()
[]
2
2
1tr ggggg
GLS
fΣ−=Σ −SSS; 1
CADF
FADF
() ()
()
() ()
[]
() () ()
[]
∑
=
−
′
−=Σ −
G
g
ggggggg
ADF
f
1
)()(; 1γσγσ sUsS
Ug()
∑
=
=g
N
r
g
ir
g
g
ix
N
x
1
)()( 1
()(
)
)()(
1
)()()( 1g
j
g
jr
N
r
g
i
g
ir
g
g
ij xxxx
N
wg−−= ∑
=
()()()(
)
)()()()()()(
1
)()()(,1g
l
g
lr
g
k
g
kr
g
j
g
jr
N
r
g
i
g
ir
g
gklij xxxxxxxx
N
wg−−−−= ∑
=