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題名 | Asymptotic Theory of a Bias-Corrected Least Squares Estimator in Truncated Regression |
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作者 | Lai,Tze Leung; Ying,Zhiliang; | 書刊名 | Statistica Sinica |
卷期 | 2:2 1992.07[民81.07] |
頁次 | 頁519-539 |
分類號 | 319.51 |
關鍵詞 | 漸近理論; 線性迴歸; Asymptotic normality; Bias-corrected estimator; Consistency; Counting process; Linear regression; Martingale; Product-limit estimator; Truncation; |
語文 | 英文(English) |
英文摘要 | Let y = □ + □ denote the intrinsic relation between the response y and a covariate vector x, where □ represents an unobservable random variable. A truncated regression model assumes the existence of another (truncation) variable t so that (x, y, t,) is observed if and only if t □ y and that nothing is observed if t > y. Tsui, Jewell and Wu (1988) have proposed a bias-corrected method to extend the classical least squares approach to regression analysis with truncated data and have found the method to perform well in an extensive simulation study. To develop an asymptotic theory for this approach, we first introduce a slight modification of their estimator to make it more tractable and then establish the consistency and asymptotic normality of the modification under certain regularity conditions. By making use of the asymptotic normality result, approximate confidence regions for β are also given. |
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