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).
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
Poisson distribution sample asymptotic MLE distribution
1. 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)
![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)](https://image.slidesharecdn.com/cananyoneexplainhowtosolvethequestioneasdetailedaspossi-230401111812-7c863873/85/can-anyone-explain-how-to-solve-the-question-e-as-detailed-as-possipdf-1-320.jpg)
