臺灣博碩士論文加值系統

摘 要
常態分布之樣本平均數及樣本變異數具有下列統計性質:(1)二者均為充分統計量.(2)二者獨立.(3)樣本平均數為
MLE , UMVUE 及動差估計式.(4)樣本變異數為 MLE ,動差估計式,經適當修正可為 UMVUE .(5)二者之變異數為
Cramer-Rao 下界.(6) 二者均為漸近有效估計式.本文探討柏努力條件下,條件樣本平均數及條件樣本變異數是否
仍有上列性質 .

Abstract
The sample mean and sample variance of a Gaussian distribution have the following nice statistical properties:(1)both are sufficient,(2)they are independent,
(3)sample mean is m.l.e., UMVUE, and method of momemt estimator,(4)sample variance is m.l.e.,method of moment estimator and UMVUE if multiplied by a constant,
(5)both estimators have variances achieve the Cramer-Rao lower bound,(6)both estimators are asymptotically efficient.Based on sample obtianed from the
conditional Gaussian distribution given Bernoulli distribution,we study conditional sample mean and conditional sample variance and check if they also have
the above statistical properties.

目 錄
第一節 簡界 ...................................1
第二節 相關係數 ...............................3
第三節 信息 ...................................6
第四節 Cramer-Rao 不等式 .....................10
第五節 Likelihood 函數及充分性 ...............12
第六節 MLE及動差估計法之有效性 ...............13
第七節 不偏性 ................................17
第八節 獨立性 ................................19
第九節 結論 ..................................22
參考資料 .....................................23

[1] 陳妙盈(1994). 兩母体含常態及二項變異數之模型的參數估計論.中央大學碩士論文.[2] Bickel,P. and Doksum,K.A.(2001).Mathematical Statistics,Vol1,2nd ed.,Prentice Hall.[3] Casella,G. and Berger,R.L.(2002).Statistical Inference,2nd ed.,Duxbury.[4] Lehmann,E.L. and Casella,G.(1998). Theory of Point Estimation, 2nd ed.,Springer.