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題 名 | 在變異數未知情形及共軛先驗分配下有界常態平均數之貝氏估計=Bayesian Estimation of a Bounded Normal Mean under Unknown Variance and Conjugate Prior |
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作 者 | 羅琪; 廖淑宛; | 書刊名 | 中國統計學報 |
卷 期 | 42:3 2004.09[民93.09] |
頁 次 | 頁245-257 |
分類號 | 319.54 |
關鍵詞 | 貝氏估計; 有界常態平均數; 有限制的貝氏估計量; 截頭的貝氏估計量; Bayes estimation; Bounded normal mean; Restricted bayes estimator; Truncated bayes estimator; |
語 文 | 中文(Chinese) |
中文摘要 | 在統計文獻上,在損失函數為平方誤差損失 (squared-error loss) 且變異數已知時,用最大概似估計量估計有界的常態平均數,此估計量既不滿足允許性(admissibility) 也不滿足大中取小性 (minimaxity)。Lo (1995) 在其論文中曾探討用貝氏法在平方誤差損失且變異數已知的情形下,估計有界的常態平均數,文中假設未受限制的母體平均數的先驗分配為無訊息 (noninformative)。另外Lo (2000) 曾探討相同的問題,但是先驗分配是取共軛分配。 然而在實務上,通常平均數未知,變異數也未知,所以假設變異數為已知並不十分合理。因此廖 (2000)將Lo (1995) 的研究,推廣到變異數未知的情形,本文則是將Lo (2000) 的研究,推廣到變異數未知的情形,兩研究皆集中於一維。本文考慮在變異數未知及共軛先驗分配下之有界常態平均數的貝氏估計。研究的內容色含後驗分配與有限制的貝氏估計量的推導、與其他估計量 (未受限制的及截頭的貝氏估計量) 的風險函數的比較及三個估計量平均損失的模擬研究。結論是貝氏法不但可以輕易地解決平均數有界的問題,而且有限制的貝氏估計量也優於另外兩個估計量。最後,並將本文結果與Lo (1995,2000)、廖 (2000) 的結果作成比較。 |
英文摘要 | It is well known in the statistics literature that the MLE is neither admissible nor minimax when we use it to estimate the bounded normal mean vector under squared-error loss and known covariance matrix. The problem of Bayesian estimation of a bounded, multivariate normal mean under squared-error loss and known covariance matrix has been considered by Lo (1995). In her research, the prior distribution of the unrestricted mean is assumed to be noninformative. For the case of using conjugate prior has been developed by Lo (2000). In practice, it is unrealistic to assume that the variance is known. Therefore, Liao (2000) has studied the problem when the variance is unknown and the prior distribution of the unrestricted mean is noninformative. This paper will consider the same problem under unknown variance and conjugate prior. The posterior distribution and the restricted Bayes estimator are obtained. Numerical results are used to compare the performance between the restricted Bayes, unrestricted Bayes, and truncated Bayes estimators. The overall conclusion is that the Bayes method can solve the bounded mean problem easily and the restricted Bayes estimator is generally superior than the other 2 estimators. Finally, the paper will relate/assimilate the results in current study with earlier results of Lo (1995, 2000) and Liao (2000). |
本系統中英文摘要資訊取自各篇刊載內容。