@HaomingJiang
2017-08-29T02:17:14.000000Z
字数 3929
阅读 1494
Name: Haoming Jiang
:
: normal distribution with variace 1 ad mean
:
:
for ,
with the fact that
Yes is inadmissible, sine
, because
I would like to use . Since for any , the risk is the same and converge to 0, when n goes to infinity.
When , if and only if
With , , so the choice gives uniformly smallest risk function.
when , . As a result for any which is better than , . Which means . So . So is admissible.
:
: binomial distribution with parameter
:
:
blue line is
red line is
yellow line is
If there exits another procedure , s.t. .
As a result
So . Which means, . As a result . So is admissible.
When n = 2, If there exits another procedure , s.t. .
As a result .
When , . So .
So .
Let . Both and converge to at the speed of . So the inquality holds, if and only if also converges to 0 at the speed of . As a result, .
So . Both sides are devided by , and the extend defination to where with the continuity. So . So .
So is addmissable.