1T
= -∑ S(Qθ (xt, Zt))CtS(Qθ(xs))fz (zt)
T t=1
1T
+-∑ CrS(Qθ(xt))S(Qθ(xs, Zs))f(Zt)
T t=1
1r
- - ∑ CTS(Qθ (xt ))S(Qθ (Xs )) f z (Zt ), (A.36)
r t=1
where Qθ(xs,Zs) is between Qθ(xs) and Qθ(Zs). Then by using the same procedures as
in (A.27), we have
J3(Qθ)-J3(Qθ-CT)=O(CT). (A.37)
Now we have the result of Step 1 for the proof of Theorem (iii). □
Step 2: Show that JT=J+op(1) under the alternative hypothesis.
Using (7) and uniform convergence rate of kernel regression estimator under β-mixing
process, we have
1 TT
T =------∑ ∑ Kεεs
Tm tsts
T(T- 1)h t=1 s≠t
1
= -∑ E(st | z)fz(zε
T t=1
= ⅛ ∑ e(ε | z ) fz(z )ε
T t=1
+1 ∑ {EE:- | zt )f (zt )- e(ε | zt ) fz(zt )} εt
T t=1
= ⅛ ∑ e(ε | zt ) fz(zt )εt+op(1)
T t=1
=e [e(ε | zt ) fz(zt ε ]+op(1)
=J+op (1)
(A.38)
□
21
More intriguing information
1. Apprenticeships in the UK: from the industrial-relation via market-led and social inclusion models2. ‘Goodwill is not enough’
3. Heterogeneity of Investors and Asset Pricing in a Risk-Value World
4. Analyse des verbraucherorientierten Qualitätsurteils mittels assoziativer Verfahren am Beispiel von Schweinefleisch und Kartoffeln
5. Integrating the Structural Auction Approach and Traditional Measures of Market Power
6. The name is absent
7. The name is absent
8. I nnovative Surgical Technique in the Management of Vallecular Cyst
9. TOMOGRAPHIC IMAGE RECONSTRUCTION OF FAN-BEAM PROJECTIONS WITH EQUIDISTANT DETECTORS USING PARTIALLY CONNECTED NEURAL NETWORKS
10. Dementia Care Mapping and Patient-Centred Care in Australian residential homes: An economic evaluation of the CARE Study, CHERE Working Paper 2008/4