中文摘要：

半参数回归模型在工程、经济和医学问题中有着广泛的应用,但是实际问题中数据往往带有测量误差,并且许多情况下解释变量和某些响应变量之间的关系是单调的,此时普通的参数最小二乘估计是有偏的,且非参数部分的估计无法保证单调性.本文针对这两个问题研究了半参数单调回归模型,得到了参数的无偏估计,同时非参数部分估计具有单调性,并得到了估计的渐近分布,因而具有较好的应用价值.随机模拟结果显示估计具有较好的有限样本性质.

英文摘要：

The semiparametric regression model is widely used in engineering,economic and medical fields.However,data collected in applications are often measured with errors,and response variables are often monotonously related to some of the explanatory variables.In such cases,ordinary least square estimator of parameters is biased and the monotonicity of the estimator of the nonparametric component can not be guaranteed.The semiparametric isotonic errors-in-variables regression model is thus considered in this paper.The proposed estimator of the parameter is unbiased and the estimator of the nonparametric component is monotone.The asymptotic distributions of the estimators are also obtained.Simulation results show that the obtained estimators have good finite-sample properties.