[問題] Casella&Berger Ex.7.3.22,p346

看板Statistics作者 (star)時間11年前 (2014/04/27 03:30), 編輯推噓0(1推 1噓 11→)
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不知道有沒有剛好版友對Casella&Berger書很熟悉或是剛好在念這段的 我有個問題想請教一下 p.346 Example 7.3.22 , 第五行 "This means that the family of pdfs of Y is complete, and there are no unbiased estimatros of zero that are based on Y. (By sufficienty, in the form of the Rao-Blackwell Theorem, we need consider only unbiased estimators of zero based on Y) 我不太懂這段為什麼是對的。 1. 我不大明白為什麼Y是complete所以there are no unbiased estimatros of zero that are based on Y. 2.為什麼need consider only unbiased estimators of zero based on Y. 前情提要: 範例是在說X1,....Xn are iid from uniform(0,θ) (n+1)Y/n is an unbiased estimator of θ, where Y=max(X1,...Xn) 但是因為某些條件不滿足，使得Cramer-Rao Thm不適用， 所以best unbiased estimator無法用CRLB這個方式 課本介紹了另一種用unbiased estimator of 0的方式去找best unbiased estimator 接下來就是我上面引的那一段了 謝謝大家的幫忙! -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 98.204.178.191 ※ 文章網址: http://www.ptt.cc/bbs/Statistics/M.1398540622.A.522.html
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04/27 09:51, , 1F
1. and譯為"而且", 不是"所以".
04/27 09:51, 1F
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04/27 09:51, , 2F
2. 那是為了符合completeness的定義.
04/27 09:51, 2F
噓
04/27 11:18, , 3F
CRLB必須符合regularity condition !
04/27 11:18, 3F
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04/27 11:19, , 4F
Support 不能與參數相關
04/27 11:19, 4F
推
04/27 11:21, , 5F
CRLB 要滿足regularity condition
04/27 11:21, 5F
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04/28 17:26, , 6F
"no unbiased...based on Y" 恐怕是有漏字, 因為 0 就是
04/28 17:26, 6F
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04/28 17:26, , 7F
0 的 unbiased estimator based on Y. 應該說:
04/28 17:26, 7F
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04/28 17:27, , 8F
"no non-constant unbiased estimator based on Y"
04/28 17:27, 8F
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04/28 17:28, , 9F
至於只考慮 based on Y, 請注意一下 Y 是否為 sufficient
04/28 17:28, 9F
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04/28 17:29, , 10F
statistic? 因為若有一 unbiased estimator (for some
04/28 17:29, 10F
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04/28 17:30, , 11F
parameter), 則有一個 based on minimal sufficient
04/28 17:30, 11F
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04/28 17:30, , 12F
statistic 的 unbiased estimator 比原 estimator 更好 (或
04/28 17:30, 12F
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04/28 17:30, , 13F
至少一樣好).
04/28 17:30, 13F
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