※ 引述《kking222》之铭言： > 令X1,...,Xn为一来自P(Xi=a-1)=P(Xi=a)=P(Xi=a+1)=1/3,且a为一整数. > 证明没有非常数的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恶之故有道者不处君子居则贵左用兵则贵右兵者不祥之器非君子 之器不得已而用之恬淡为上胜而不美而美之者是乐杀人夫乐杀人者则不可得志於天下 矣吉事尚左凶事尚右偏将军居左上将军居右言以丧礼处之杀人之众以哀悲泣之战胜以 丧礼处之道常无名朴虽小天下莫能臣侯王若能守之万物将自宾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将知止知止可以不殆譬道之在天163.13.113.180海