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題 名 | 部分排序在有測量誤差的共變異數分析的應用=Application of Partial Ranks to Analysis of Covariance with Measurement Errors |
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作 者 | 陳主智; 郭曉蘋; | 書刊名 | 中國統計學報 |
卷 期 | 34:1 1996.03[民85.03] |
頁 次 | 頁25-40 |
分類號 | 319.3 |
關鍵詞 | 部分排序; 測量誤差; 模式誤認; 最小平方法; 漸近相對效率; Asymptotic relative efficiency; Measurement errors; Ordinary least squares; Partial ranks; |
語 文 | 中文(Chinese) |
中文摘要 | 在共變異數分析 (Analysis of Covariance,簡稱ANOCOVA) 中,使用有測量誤差 (measurement errors,簡稱ME) 的共變數 (covariables) 來檢定群體差異(growp difference) 會使得檢定力 (power) 降低。在此情況下,針對一般而言,較其它統計量有較佳檢定效率 (test efficiency) 的最小平方法 (ordinary least squares,簡稱OLS),Carroll (1989) 提出一個公開的問題:「是否有其它統計量在較弱的假設下可以有比最小平方檢定更佳的檢定效率?」在本文中,我們提出以修正測量誤差的部分排序 (partial ranks),取代排序共變異數分析 (Quade (1967)) 中共變數的排序值。模擬實驗的結果顯示,在相加型測量誤差模式(additive ME model) 的假設下,我們可以大幅提高其相對於最小平方法的檢定效力,此種情況在當有誤差的共變數的分布相當偏斜 (skewed) 及其與反應變數的關係為非線性時尤然。不僅如此,結果亦顯示在正值的相乘型的測量誤差模式(multiplicative ME model),部分排序的共變異數分析亦較最小平方法有較佳的檢定效力。 |
英文摘要 | In a balanced analysis of covariance (ANOCOVA), it is known that the ordinary least squares (OLS) estimate for treatment difference with measurement errors (ME) in the covariable will have lower power than that of the estimate obtained when using the true covariable (Cochran (1968); Degracie and Fuller (1972)). Following the conclusion that the OLS test in general has better efficiency than other tests (Carroll7Gall0,and Gleser (1985)), Carroll (1989) raised an open problem that "whether there are weak assumptions which enable one to construct tests with better power than the OLS test?" In this paper, we try to answer this question through nonparametric approach using rank ANOCOVA (Quade (1967)), and to propose a new ranking method utilizing partial ranks to correct effects from the ME. The simulation results show that under the additive ME model, the proposed ranking method has better empirical power than that of the OLS test when ME is skewed. The superiority in power can be substantial in the presence of mismodelling. Under the positive multiplicative ME model, the ranking method has better empirical power than that of the OLS test for all the cases investigated. |
本系統中英文摘要資訊取自各篇刊載內容。