Testing the Information Matrix Equality with Robust Estimators



where the first line uses (1 + x)/(1 + y) 1 + x — y for x and y small,
with
x = EFn (Y2) 1 and y = σ2n 1, and the second line uses the second
moment of Student’s
t, pn/(pn 2). We also have that

Fn 4   - 3 = EFn (Y4)(1 - 2(σ2 - 1)) - 3 + o(pn 1)
σn

3 P 2n        Σ    Σ1    , l n n 1λ

—  7------7√77------77 I 1--I 3 + O(pn )

(pn 2)(pn 4)    pn J

18 3∑1     ,

= — ---1 + O ( P-1 ),                        (19)

pn

where the first line uses (1 + x)n2 1 2x and the second line uses the
fourth moment of Student’s
t, 3pП(pn 2)n 1(pn 4)n 1. Using (18) and (19),

EFn ( m 3) = ( EFσP3) 6 ( EFσY1 ɪ)
σn              σ σn

6 , z-H

= — + o ( P- )

and

EFn ( m 1)


EF^2)! Λ — dEFn (rh3)
σn       /

= 2~^ (4 1 12d)+ o(pn 1)
2 pn

To compute Σ1, note that, by partial integration and using φ'(z) = —zφ(z),

E [ZPc(Z)] = j∞ (z)dpc(z)

= У Pc ( Z )( φ ( Z ) — Z 2 φ ( Z )) dz

= E [Z2Pc(Z)] — bc

Along the same lines we get

E [Z2PC(Z)] = E [Z3pc(Z)] 2E [Zp'c(Z)] ,

and

E [Z3Pc(Z)] = 3E [Z2Pc(Z)] + E [Z4Pc(Z)] ,
28



More intriguing information

1. Constructing the Phylomemetic Tree Case of Study: Indonesian Tradition-Inspired Buildings
2. The name is absent
3. The name is absent
4. The Context of Sense and Sensibility
5. The name is absent
6. The Prohibition of the Proposed Springer-ProSiebenSat.1-Merger: How much Economics in German Merger Control?
7. The name is absent
8. THE EFFECT OF MARKETING COOPERATIVES ON COST-REDUCING PROCESS INNOVATION ACTIVITY
9. DISCRIMINATORY APPROACH TO AUDITORY STIMULI IN GUINEA FOWL (NUMIDA MELEAGRIS) AFTER HYPERSTRIATAL∕HIPPOCAMP- AL BRAIN DAMAGE
10. Portuguese Women in Science and Technology (S&T): Some Gender Features Behind MSc. and PhD. Achievement