Cl: For any δ > 0 and some mo ∈ M there is an 6> 0 such that
sup P (zn(mo) > e) ≤ δ.
n
C2: For any δ > 0 and e > 0 there is a ξ > 0 such that
sup P
n
sup ∖zn(m1)
∖J∣m1-m2∣∣<ξ
Zn(m2)∖ > 6
)≤δ
Verifying Cl and is C2 is what we set out to do. Note that Cl holds trivially as
zn(mo) = 0p(l) by Theorem 3.2 of Park and Phillips (2001). Next choose ξ < 1
and let Hj (m1j,m2j,Xj,t) = Wj(xj,t) [exp (m1Φ(xjιt)) — exp (m2Φ(xj∙,t))]. Condition
C2 follows from the continuity of A(ao,m) and the fact that
< sup n 1/4
I∣m1-m2∣∣<ξ
n J
ΣΣHj (m1,j ,m2,j ,Xj,t) ut
t=1 j=1
—
≤ ξC,
(A7)
for some C < ∞. The last result can be established as follows:
< sup n 1Z4
I∣m1-m2∣∣<ξ
n J
ΣΣHj (m1,j ,m2,j ,xj,t} ut
t=1 j=1
ξexp {(1 + sup ∣∣m∣∣) (sup ∖φ^∖)}∑ E |-
1/4
∑ wj (xjt)Ut f
t=1 J
(A8)
ξ exp J (1 + sup ∣∣m∣∣ ) (sup ∣Φ(s)∣
I ∖ тем J ∖ S
)}∑ ∣e ^-1/4 ∑ wj (xj’t)u
1/2
ξ eχp {(1+ sup ∣∣m∣∣) (sup ∖Φ(s)∖)⅛ (e∣:-■• ∑
u2 ∖ ʃt-ɪ)^l /
{(1+ sup ∖∖m∖∖) (sup ∖Φ(s)∖)}∑ (e(V∙∑ «x,,,)}'■'
where the first inequality is due to equation (B9) in Bierens (1990), and second one
is due to Liapunov’s inequality. The last term above is:
∑ E (n-1'2 ∑ w,fe,)A
j=1 ∖ t=1 J
j n Γ∞
= ∑--*'2∑ /
j=1 t=1 ∙7-∞
wj (t1'2 x)dj,t(x)dx
j
= Σ--1'2
j=1
n ∞o
^2-ll∖
t=1 j-∞o
w2(s)djιt(s∕t1'2)ds
j
2 У sup sup
. 1 t>1 X
J=1 -
z∞
-∞
w2(s)ds + o(1) < ∞,
20
More intriguing information
1. Impacts of Tourism and Fiscal Expenditure on Remote Islands in Japan: A Panel Data Analysis2. The name is absent
3. The Institutional Determinants of Bilateral Trade Patterns
4. Distortions in a multi-level co-financing system: the case of the agri-environmental programme of Saxony-Anhalt
5. Effects of a Sport Education Intervention on Students’ Motivational Responses in Physical Education
6. The name is absent
7. Iconic memory or icon?
8. The name is absent
9. FDI Implications of Recent European Court of Justice Decision on Corporation Tax Matters
10. Monopolistic Pricing in the Banking Industry: a Dynamic Model