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DEFINITION
: The sequence of estimators
̂
n
:
n
1,2,...
is
n

asymptotically normal
if
n
̂
n
−
d
→
Normal
0
,
C
, all
∈
Θ
where
C
is a
p
p
positive semidefinite matrix for all
.
∙
The matrix
C
is usually called the
asymptotic variance
of
n
̂
n
−
.
∙
Because
n
̂
n
−
converges in distribution it is also
O
p
1
.
Therefore, any
n
aysmptotically normal estimator is necessarily
n
consistent.
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