Testing the Information Matrix Equality with Robust Estimators



Further,


EFn(Y) = γnφ(0),
E
Fn(Y2)=1+γn + o(γn),
E
Fn(Y 3) = 6γnφ(0) + o(γn),
E
Fn(Y4)=3+6γn+o(γn).

Therefore, letting ( m 1 ,m 2 ,m 3) ' = Wm ( Y ; θn ),
and, upon replacing
γn with ey∕n,

EFn ( m 3)  = EFn

I
--X

sq I

Jλ

×---z

EFn ( m 2)  = EFn

I                                           I

X---X

sq I

Jλ
×---z

EFn ( m^ 1) = EFn

IX )

_

3

_

2

_


6EFn


3EFn


(Y - βn λ

σn J


2

+3=o(γn),


Y—βn = 3 Ynφ (0) + О ( Yn ),


σn


1 - dEFn ( m 3 ) = o ( Yn ),


0

b = lim ∕EFΓ[W [ Wm ( Y ; θn, )] = e   3 φ (0)

n→∞                      0

Hence bV+b = -⅛ e2.

Appendix C

Local asymptotic power of score test

First, we review briefly how the local asymptotic power of the score test
against specified alternatives can be defined. By an appropriate extension
of
f ( ; ), let the density under the alternative be f ( y ; ω ), depending on
an extended parameter
ω, and let s ( y ; ω ) = ∂ω log f ( У ; ω ). Write the
null hypothesis as
H0 : ω Ω0, where Ω0 is a restricted parameter space
(essentially, Θ). Let
ω be the restricted ML estimator (essentially, θ), i.e. ω
solves

n

max    log f (Yi; ω).

ωΩo

i=1

31



More intriguing information

1. Learning-by-Exporting? Firm-Level Evidence for UK Manufacturing and Services Sectors
2. Auctions in an outcome-based payment scheme to reward ecological services in agriculture – Conception, implementation and results
3. The name is absent
4. XML PUBLISHING SOLUTIONS FOR A COMPANY
5. European Integration: Some stylised facts
6. The Context of Sense and Sensibility
7. The magnitude and Cyclical Behavior of Financial Market Frictions
8. The name is absent
9. An Efficient Secure Multimodal Biometric Fusion Using Palmprint and Face Image
10. Demographic Features, Beliefs And Socio-Psychological Impact Of Acne Vulgaris Among Its Sufferers In Two Towns In Nigeria