Empirical likelihood inference of parameters in nonlinear EV models with censored data

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• 作者：Liandi Fang ; Yongfeng Wu
• 关键词：empirical log ; likelihood ; censored data ; error ; in ; variables ; validation data
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,489 KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

In this paper, the authors consider nonlinear error-in-variables regression models with right censored data. Based on the validation data, the authors use the Kaplan-Meier estimate and kernel estimate to repair the censored response variable Y and explanatory X with measurement error. Based on the repaired data, the authors introduce an auxiliary vector suitable to define an estimated empirical log-likelihood function of the unknown parameter which has an asymptotic weighted sum of the \(\chi_{1}^{2}\) variables. Using the result the authors can construct the asymptotic confidence regions of β. But the method of estimating weights will reduce the precision of the confidence regions. Further, the authors adjust the preceding log-likelihood, and it is shown that the adjusted empirical log-likelihood has the asymptotic standard \(\chi_{1}^{2}\) distribution. The result can be used to construct the confidence regions of β.