Statistics Graduate Level Quiz
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ASYMPTOTIC THEORY
Question 1
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PASSAGE
Define
T
(
F
)
=
E
F
(
X
2
)
/
E
F
(
X
)
T(F)=E_F(X^2)/E_F(X)
T
(
F
)
=
E
F
(
X
2
)
/
E
F
(
X
)
, where
E
F
(
X
)
=
2
E_F(X)=2
E
F
(
X
)
=
2
and
E
F
(
X
2
)
=
5
E_F(X^2)=5
E
F
(
X
2
)
=
5
. Consider contamination at
z
=
4
z=4
z
=
4
.
Using the first-order contamination derivative, what is
IF
(
4
;
T
,
F
)
\operatorname{IF}(4;T,F)
IF
(
4
;
T
,
F
)
?
A
1.5
1.5
1.5
, because only the contamination effect on the numerator remains after centering.
B
8.0
8.0
8.0
, because the contamination contributes its squared value relative to the first moment.
C
5.5
5.5
5.5
, because the numerator derivative is divided by the original first moment.
D
3.0
3.0
3.0
, because both the numerator and denominator change under contamination.
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