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Statistics
Statistics Pulse
Five questions across 6 topics. No timer.
1 / 5
Statistics
Question 1 of 5
foundation (2/10)
state theorem
For estimator
T
n
of
θ
, the mean squared error is
MSE
θ
(
T
n
)
=
E
θ
[(
T
n
−
θ
)
2
]
. What is its decomposition?
Hide and think first
A.
MSE
=
bias
2
⋅
Var
. Bias and variance multiply because they are independent error sources.
B.
MSE
=
Var
when
T
n
is consistent, since consistency forces the bias term to vanish.
C.
MSE
=
bias
2
+
Var
. Bias enters squared because the cross-term integrates to zero.
D.
MSE
=
bias
+
Var
. Both contributions are added directly without squaring.
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