Using the fact that tr (A ® B) = tr (A) tr (B) and the Cauchy-Schwarz inequal-
ity, we have
T12 XX tr(
Gx,T (xit xi) (χis xi) Gx,T
®Gx,T (xit xi) (xis xi) Gx,T
⅛∑ E©tr £Gx,T (Xit
xi) (xis
Xi)0 Gχ,τ]}
T X ∣∣Gχ,τ (xit
t
xi)k
Similarly,
T12 XXtr(
Gx,T (xit xi) (xis xi) Gx,T
®Gx,T (xis xi) (xit xi) Gx,T
T X ∣G∙,T (xi.
t
- xi )k2
and
1 XX tr f Gx,T (xit — xi) (xit — cci)° GX,T
T2 tl s' × ®Gx,T (xis - xi) (xis - xi) Gx,T
= (T X
tr Gx,T (xit
- xi) (xit
T X ∣∣Gχ,T (xit
t
- xi)k2
Thus, the right hand side of (84) is less than or equal to
3M1 κ4v sup sup E
i,T 1≤t≤T
T X ∣∣Gχ,T (xit
t
— xi)k2
Note that
sup sup E
i,T 1≤t≤T
2
T X ∣∣Gχ,t (xit — xi)k2
t
≤ sup sup E
i,T 1≤t≤T
2
T X l∣Gχ,Txitk2
t
≤ M supi,T sup1≤t≤T E ∣D1Tx1,it ∣4 + supi,T sup1≤t≤T E ∣x2,it ∣4
+supi,Tsup1≤t≤TE∣x3,it∣4
53
More intriguing information
1. The Demand for Specialty-Crop Insurance: Adverse Selection and Moral Hazard2. A Critical Examination of the Beliefs about Learning a Foreign Language at Primary School
3. Convergence in TFP among Italian Regions - Panel Unit Roots with Heterogeneity and Cross Sectional Dependence
4. Transfer from primary school to secondary school
5. Structural Breakpoints in Volatility in International Markets
6. LIMITS OF PUBLIC POLICY EDUCATION
7. A Unified Model For Developmental Robotics
8. Biological Control of Giant Reed (Arundo donax): Economic Aspects
9. Financial Development and Sectoral Output Growth in 19th Century Germany
10. A simple enquiry on heterogeneous lending rates and lending behaviour