中文摘要：

该文考虑非线性半参数回归模型,构造了模型中未知参数的经验对数似然比统计量,证明了所提出的统计量具有渐近χ2分布,由此结果可以用来构造未知参数的置信域.另外,该文也构造了未知参数的最小二乘估计量,并证明了它的渐近性质.仅就置信域精度及其覆盖概率大小方面,通过模拟研究比较了经验似然方法与最小二乘法的优劣.

英文摘要：

In this paper,we consider the nonlinear semiparametric regression model,and construct the empirical log-likelihood ratio statistic for the unknown parameter.It is shown that the proposed statistics have the asymptotic standard chi-square distribution,and hence it can be used to construct the confidence region of the parameter.In addition,the least squares estimator of unknown parameter is constructed,and its asymptotic behavior is proved. A simulation study is carried out to compare the proposed methods with the least-squares method in terms of the confidence regions and its coverage probabilities.