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研究生:張克聞
研究生(外文):Ke-Wen Chung
論文名稱:參數模式中秩序統計量之費雪訊息
論文名稱(外文):The Fisher Information Of Order Statistic In Parametric Model
指導教授:陳重弘陳重弘引用關係
指導教授(外文):Chong-Hong Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:60
中文關鍵詞:費雪訊息秩序統計量指數分配族
外文關鍵詞:order statisticsFisher informationfamily of exponential distribution
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本篇論文主要在研究秩序統計量(order statistic)之費雪訊息。對於任何參數之實數值函數之不偏估計量,其變異數,不論正規條件是否滿足,必存在一下界,亦即為訊息不等式(information inequality)。由此進而可評估此不偏估計量之好壞,當然對參數是為多維度時亦可成立。
在此論文中,我們將說明為何統計量所包涵的訊息數越大,則由此統計量來估計未知參數,將可得較好之結果,
同時本文主要討論,秩序統計量之訊息數,或訊息矩陣。
此外由所得之訊息數或訊息矩陣來了解秩序統計量所包涵之訊息之大小,亦即當樣本數固定時,何處之秩序統計量相對的包涵較多之訊息數。
The purpose of this research is to consider the Fisher information of order statistic. For any unbaised estimator T of real-value function there exists a lower bound for var(T), namely information inequality under regularity assumptions. Also, a similar lower bound exists when these regularity assumptions do not hold. Without loss of generality, we can extend this inequality to multiparameter case. In this paper, we discuss that why more accurately that real-value function of unknow parameter can be estimated when unbaised estimator has larger information. Mainly, we derive the Fisher information or information matrix of order statistics under the family of exponential distribution, for example I_{X_{i:n}},
I_{(X_{r_{1}:n},X_{r_{1}+1:n},cdots,X_{r_{2}:n})} ... etc. Some of them, provide optimal informations.
1 緒論.......................................2
2 訊息不等式及其含意.........................3
3 指數分配的基本性質和簡單的結果.............9
4 位置參數己知,尺度參數未知之費雪訊息數.....15
5 位置參數未知之訊息數......................38
6 結論......................................48
附錄
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[2] Chapman, D. G. and Robbins, H. (1951) , ”Minimum variance estimation without regularity assumptions.” Ann. Math. Statist. 22 ,581-586.
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[10] Johnson, N. L. , Kotz, S. and Balakrishnan, N. (1994) , Continuous Univariate Distribution-Volume 1, Second edition, John Wiley & Sons, New York.
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[12] Lehmann, E. L. (1983) , Theory of Point Estimation, John Wiley & Sons, New York.
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[14] Rao, C. R. (1947) , ”Minimum variance and the estimation of serveral parameters.” Proc. Camb. Phil. Soc. 43 ,280-283.
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[16] Robert V. Hogg and Allen T. Craig (1995) , Introduction To Mathematical Atatistics, Fifth edition, A Simon & Schuster Company, New Jersey.
[17] Shao, J. (1999) , Mathematical Statistics, Springer , New York.
[18] Savage, L. J. (1954,1972) , The foundations of statistics., Wiley, New York. Rev. ed.,Dover Pulications.
[19] Savage, L. J. (1976) , ”On rereading R.A. Fisher (with discussion).”Ann. Statist. 4 ,441-500.
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