Asymptotic Methods in Statistical Inference - Statistics Centre

191
• The MLE is not the only efficient estimator, for
instance ‘+
³
−12´’ isalsoefficient. A
less trivial example is if 1 ∼ ³ = 2´
for a known (= 1). To obtain the MLE ˆ
it is convenient to first obtain ˆ, where =1.
We define 2 = P 2 and calculate
(
() ∝ − exp − 1 X ( − ) 2 )
2 2 ½
= exp − 1 X
( − ) 2¾
2
() = + log − 1 2 2 2 + ¯
0 () =
(
1
− 2 + ¯
and then
)
ˆ =
r ³
¯ + ¯´2 +42
2 2
ˆ = 1ˆ = s µ
2 ¯ 2
+ 2 − 2 ¯