作者ww770829 (新庄西盛教会)
看板Grad-ProbAsk
标题Re: [问题] Hogg数统一题
时间Fri May 8 20:59:54 2009
※ 引述《njg (njg)》之铭言：
: 是Hogg的6.2-14 @@"
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: Let s^2 be the sample variance of a random sample of size n>1
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: from N(μ,σ^2) , 0<θ<∞ , where μ is unknown. We know E(s^2)= θ.
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: a)What is the efficiency of s^2
: ^
: b)Under these conditions, what is the mle θ of θ
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: 先谢谢大家^^"
:
令Y=(n-1)S^2/θ~x^2(n-1)
V[(n-1)S^2/θ]=2(n-1) =>V(S^2)=2θ^2/(n-1)
f(x|θ)=(2πθ)^(-1/2)exp{-(x-u)^2/2θ}
d^2lnf(x|θ)/dθ^2=(2θ^2)^(-1)-(x-u)^2/θ^3
I(θ)=-E[(2θ^2)^(-1)-(x-u)^2/θ^3]=-(2θ^2)^(-1)+V(X)/θ^3=(2θ^2)^(-1)
V(S^2)=2θ^2/(n-1)≠1/nI(θ)
S^2之变异数不等於C-R Lower Bound 故不具有效性
※ 编辑: ww770829 来自: 61.228.43.233 (05/12 16:03)