and
aσ2 Ih=
∂ d
aσ2 ∣H0=
∂ tt I
∂λ I н§
Jt In,
It (B,B)-∖
∂2vIτ (B'B}-∖W'B + b'w)(b'b)-∖
where B = Iχ — ATU and A is the MLE of A under Hq. Using (A.2), we get
¾=H L = -⅛γU-b)+⅛,ι⅛ (≡)2]≡∙
°σμ l¾ ^crz√
This uses the fact that
(A.25)
(A.26)
(A.27)
(A.28)
"1⅛∣H= = ⅛iτ BtB)(jτ in) = ⅛jt b'b,
dσμ IHg σv σv
d⅛ d∣ff. = (⅛⅛ -B'B)(⅛⅛ B∙B) = ±jτ (B,B)2,
JO и I ∕ι∩ (7 (7 (7
μ и u is -id 'j is
tr[ "⅛L∙ = ⅛trljτ ≡] = ⅛r[B'B].
m∕< IH0 σ,j σi7
Similarly
<9L I TN 1 ʌ,r .^, ʌ,,ʌ
(A.29)
~w =—zτ S—τ~∖u [It (B B)]u = 0,
5σ2∣H0= 2⅛ 2⅛
which yields
λ2 _ u'[Iτ B'B]u
σv ~ TN ’
This uses the fact that
d⅛. = ⅛⅛ bNjt (S'SN) = ^τ ⅛
U O °, у u is
^∖ll, = Ji1τ ικ)(Iττ B'B) = τlτ b'b.
(J(J ,, I ∕ι∩ (7 (7 (7
Z√ 0'-7i√ l7 у u is
Γ -lljfl∣ = tn
l u ∂σl jIh0= Bl ∙
Also,
24