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題 名 | 有界多維常態平均數的貝氏估計=Bayesian Estimation of a Bounded Multivariate Normal Mean |
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作 者 | 羅琪; | 書刊名 | 中國統計學報 |
卷 期 | 38:2 2000.06[民89.06] |
頁 次 | 頁215-230 |
分類號 | 319.5 |
關鍵詞 | 允許性; 有界多維常態平均數; 有限制的貝氏估計量; 貝氏估計; 截頭的貝氏估計量; Admissibility; Bayesian estimation; Bounded multivariate normal mean; Restricted Bayes estimator; Truncated Bayes estimator; |
語 文 | 中文(Chinese) |
中文摘要 | 在損失函數為二次方下,用貝氏法估計有界的多維常態平均數的問題已於Lo (1995) 中探討,論文中假設母体平均數的先驗分配為無訊息 (noninformative)。本文探討相同的問題,在母体平均數的先驗分配為常起分配的假設下,證明有限制的貝氏估計量其允許性 (admissibility)。數值的結果用來比較有限制的貝氏估計量、傳統的沒有限制的貝氏估計量及截頭的貝氏估計量。結論是有限制的貝氏估計量優於另外兩個。另外當維數愈高時,有限制的貝氏估計量的表現愈好。 |
英文摘要 | The problem of Bayesian estimation of a bounded multivariate normal mean under quadratic loss has been considered by Lo (1995) . Lo considered the prior distribution of the unrestricted mean which is noninformative. The present paper treats the case that the prior distribution of the unrestricted mean is normal. The restricted Bayes estimator is obtained and it is proved that this estimator is admissible. Numerical results are used to compare the performance between the usual unrestricted Bayes estimator, the restricted Bayes estimator and the truncated Bayes estimator. The overall conclusion is that the restricted Bayes estimator is generally superior and the trend becomes more evident as the dimension increases. |
本系統中英文摘要資訊取自各篇刊載內容。