核实数据下非线性EV模型中经验似然降维推断

摘要

In the article, we consider the nonlinear error-in-response models with the help of validation data. Using semiparametric dimension reduction to construct the estimated empirical likelihood and adjusted empirical likelihood of the unkown parameter, it is shown that the estimated empirical log-likelihood has the asymptotics weighted sum of chi-square variables distribution and adjusted empirical log-likelihood has the asymptotic standard chi-square distribution. The result can be used to construct the confidence regions of the unknown parameter.%本文研究了响应变量有误差的非线性模型.应用半参数降维技术构造未知参数的被估计经验似然及调整的经验似然,证明了所提出的被估计的经验对数似然与其调整的经验对数似然分别渐近于独立卡方变量加权和的分布与标准卡方分布,所得结果可用来构造未知参数的置信域.