[機統] 97政大

看板Math作者 (FLY)時間14年前 (2012/02/11 15:19), 編輯推噓2(2推 0噓 7→)
留言9則, 2人參與, 最新討論串1/1
1.Let X1,X2,.....,Xn be a random sample from EXP(Θ,η) , and let Zi=(Xi-η)/Θ Find the BLUEs (Best Linear Unbiased Estimator) for Θ andη . 2.Consider a random sample of size n form a population with pdf: f(x)=p(1-P)^(x-1), 0<p<1 x=1,2,3... b)Show that (ΣXi/n-1)/(ΣXi/n)^2 converges in probability to p(X=2) (機率收斂有沒有類似MLE的不變性) c)Find the asymptotic distribution of (ΣXi/n-1)/(ΣXi/n)^2 ΣXi/n=bar(Xn) -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 59.112.86.60
推
02/11 21:06, , 1F
2(b)用一個事實：X_n機率收斂到X、Y_n機率收斂到Y，
02/11 21:06, 1F
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02/11 21:07, , 2F
則X_nY_n機率收斂到XY。利用(a)1/bar(X_n)->p，可以
02/11 21:07, 2F
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02/11 21:08, , 3F
知道1/(bar(X_n))->p^2 in probability。因此可以
02/11 21:08, 3F
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02/11 21:09, , 4F
推得原式會機率收斂到P(X=2)=(1-p)p
02/11 21:09, 4F
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02/11 21:10, , 5F
ps (a)小題是要證bar(X_n)機率收斂到P(X=1)=p
02/11 21:10, 5F
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02/11 21:12, , 6F
(c)我覺得應該是服從常態，mean是該式的參數，
02/11 21:12, 6F
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02/11 21:12, , 7F
variance是該式的CRLB
02/11 21:12, 7F
推
02/11 21:15, , 8F
筆誤...應該是1/(bar(X_n))^2->p^2
02/11 21:15, 8F
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02/11 22:38, , 9F
感謝幫忙
02/11 22:38, 9F
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