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題名 | 有限樣本之母體分配假設的訊息矩陣檢定=Information Matrix Tests for Population Distribution Hypothesis in Finite Samples |
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作者 | 洪來發; 王文中; | 書刊名 | 中華心理學刊 |
卷期 | 43:1 2001.06[民90.06] |
頁次 | 頁35-44 |
分類號 | 170 |
關鍵詞 | White訊息矩陣檢定; Lancaster人工迴歸式; 有限樣本; 母體分配; White information matrix test; Lancaster artificial regression; Finite samples; Population distributions; |
語文 | 中文(Chinese) |
中文摘要 | 母體分配的假設是各重要的議題。如果當初關於母體分配的佑設不恰當,後續的統計推論都將失真。本研究探討了White(1982)母體分配假設的訊息矩檢定法(information matrix text)及其相關的檢定法。鑑於核檢定法必須計算logdensity之第三階偏導數以求得共變異矩陣,因此推演困難且繁雜,並不實用。Chesher (1983)與Lancaster(1984)提出人工迴歸式的算單計算公式,不需計簡▽D(θ),就能估算出White訊息矩陣統計檢定式等於樣本大小n乘以判定係數R2。由於該人工迴歸式不適用於▽D(θ)為0的情境,因此我們提出了適用於▽D(θ)為0時,和Lancaster計算式不同的統計檢定式。由於訊息矩陣檢定法,牽涉到許多估計式,在尚無嚴謹理論佐證下,我們藉由模擬分析來評斷各檢定式之第一型誤差,結果顯示Lancaster人工迴歸檢定法傾向於過度拒絕虛無假設,White檢定法結果是三者中最令人滿意的,我們的檢定法結果介於兩者之間,這說明了我們的檢定法簡單有效。 |
英文摘要 | This study attempts to explore the issues in hypothesis testing of population distributions, based on Whites’ information matrix test (White, 1982). We point out that White’s ▽D(θ) method requires the computation of the third derivatives of log-density for finding the covariance matrix, which is very labor-intensive and impractical. Chesher (1983) and Lancaster (1984) developed a simpler method of artificial regression where the computation is no longer needed. It is found that White’s ω is equal to sample size n multiplied by the coefficient of determination R2. However, their method is improper when ▽D(θ)=0. Accordingly, we propose another estimator to correct the errors in the artificial regression. Without strong theoretical evidence, these three methods are compared through a simulation study in terms of type I error rates. The results show that the artificial regression method tends to over-reject the null hypothesis, White’s method yields very satisfactory results. Our method is between these two methods in performance, indicating that our method is simple and effective. |
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