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@HaomingJiang 2017-08-28T18:17:14.000000Z 字数 3929 阅读 1393

ISYE 6412 HW #1

Name: Haoming Jiang


Problem #1

(a)

:
: normal distribution with variace 1 ad mean
:
:

(b)

for ,
with the fact that







hw11.PNG-32.3kB

(c)

Yes is inadmissible, sine

(d)

, because

(e)


hw12.PNG-26.3kB

hw12.PNG-26.3kB

h13.PNG-12.6kB

hw14.PNG-23.2kB

(f)

I would like to use . Since for any , the risk is the same and converge to 0, when n goes to infinity.

(g)

When , if and only if

With , , so the choice gives uniformly smallest risk function.

(h)

when , . As a result for any which is better than , . Which means . So . So is admissible.

Problem #2

(a)

:
: binomial distribution with parameter
:
:

(b)




hw15.PNG-30.6kB
blue line is
red line is
yellow line is

(c)

If there exits another procedure , s.t. .

As a result
So . Which means, . As a result . So is admissible.

(d)

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.

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