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Can anyone explain how to solve the question e) as detailed as possi.pdf
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Can anyone explain how to solve the question e) as detailed as possible? Suppose X=(X1,X2,,Xn) is a random sample from Poisson () with probability distribution f(x;)=P(X=x)=x!ex,x=0,1,2,;>0. (a) Show that W=2I{X1=2}(X) is an unbiased estimator of ()=2e. (b) Argue that T=i=1nXi is complete and sufficient for . (c) Derive the umvue ^ for ()=2e. (d) What is the MLE ~ of () ? (e) State the asymptotic distribution of n(~()). (e) Since: 22lnL(X,)=21i=1nxiIX()=E[22lnL(X,)]=n which is also IX(), so IX1()=1. Also: ()=2e2e=e(2). The delta method implies: n(~())dN(0,3e2(2)2).
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Can anyone explain how to solve the question e) as detailed as possi.pdf
- Can anyone explain how to solve the question e) as detailed as possible? Suppose X=(X1,X2,,Xn) is a random sample from Poisson () with probability distribution f(x;)=P(X=x)=x!ex,x=0,1,2,;>0. (a) Show that W=2I{X1=2}(X) is an unbiased estimator of ()=2e. (b) Argue that T=i=1nXi is complete and sufficient for . (c) Derive the umvue ^ for ()=2e. (d) What is the MLE ~ of () ? (e) State the asymptotic distribution of n(~()). (e) Since: 22lnL(X,)=21i=1nxiIX()=E[22lnL(X,)]=n which is also IX(), so IX1()=1. Also: ()=2e2e=e(2). The delta method implies: n(~())dN(0,3e2(2)2)
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