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Asymptotic Statistics
Asymptotic Statistics
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MLE is consistent under regularity conditions (identifiability, compact parameter space, uniform LLN). Which of the following is a well-known example where MLE is NOT consistent?
Hide and think first
A.
Estimating the mean of
N
(
μ
,
1
)
:
X
ˉ
is the MLE and it is biased away from
μ
B.
Logistic regression with perfectly separable classes, where the MLE diverges to infinity
C.
The Neyman-Scott problem, where MLE of
σ
2
converges to
σ
2
/2
as
n
→
∞
D.
Poisson regression with a log link: the non-linear link function breaks the consistency proof
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