Re: [問題] 求助一題UMVUE...
※ 引述《kking222》之銘言：
> 令X1,...,Xn為一來自P(Xi=a-1)=P(Xi=a)=P(Xi=a+1)=1/3,且a為一整數.
> 證明沒有非常數的g(a)有UMVUE.
Pf.
Let E[U(X)]=0 for all a
=> 1/3(U(a-1)+U(a)+U(a+1))=0 for all a
=> U(a-1)+U(a)+U(a+1)=0 for all a
If d(X) is UMVUE of g(a), then
E[d(X)U(X)]=0
=>1/3[d(a-1)U(a-1)+d(a)U(a)+d(a+1)U(a+1)]=0
=>d(a-1)U(a-1)d(a)U(a)+d(a+1)U(a+1)=0, for all U
Let U(a-1)=1, U(a)=-1, U(a+1)=0
then d(a-1)=d(a) for all a
=>d is constant.
and d is unbiase of g(a), so g(a) is constant.
--
夫兵者不祥之器物或惡之故有道者不處君子居則貴左用兵則貴右兵者不祥之器非君子
之器不得已而用之恬淡為上勝而不美而美之者是樂殺人夫樂殺人者則不可得志於天下
矣吉事尚左凶事尚右偏將軍居左上將軍居右言以喪禮處之殺人之眾以哀悲泣之戰勝以
喪禮處之道常無名樸雖小天下莫能臣侯王若能守之萬物將自賓天地相合以降甘露民莫
之令而自均始制有名名亦既有夫亦將知止知止可以不殆譬道之在天163.13.113.180海
討論串 (同標題文章)
完整討論串 (本文為第 2 之 2 篇)：