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題名 | Jackknife Methods for Truncated Data=截取資料下之摺刀法 |
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作者 | 沈葆聖; 林明杰; | 書刊名 | 東海管理評論 |
卷期 | 3:1 2001.07[民90.07] |
頁次 | 頁173-185 |
分類號 | 319.5 |
關鍵詞 | 截取資料; 摺刀法; Truncation; Jackknife; |
語文 | 英文(English) |
中文摘要 | 令X和Y分別表示兩獨立之連續變數具存活函數□和□。在截取資料下,僅在X≽Y時,方可同時觀察到X和Y。Lynden-Bell (1971)提出□(x)的非參數最大概似估計值(nonparametric MLE),□,其中□(z)為累積危險函數估計值。本文中,我們推導去除d個的□(z)摺刀估計值。依此,減低□(x)的估計偏差。此外,證明□(x)去除一個的摺刀雙方估計收斂至真正變方。 |
英文摘要 | Let X and Y be two independent positive random variables with survival functions □ and □, respectively. Under random truncation, X and are both observable only when X is large than Y. The nonparametric MLE of □(x), □, was derived by Lynden-Bell (1971), where □(z) is the estimated cumulative hazard function. In this note, we derive an explicit formula for the delete-d jackknife estimate of □(z). From this it is demonstrated that jackknifing may lead to a reduction of the bias. Besides, it is shown that the delete-1 jackknife variance estimator of □(x) consistently estimates the limit variance. |
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