带有核实数据的误差在协变量线性模型的估计

Estimation of linear error-in-covariables models with validation data

考虑协变量有误差的线性模型Y=Xτβ+e,在许多实际问题中,准确测得感兴趣的变量可能是很困难的,或者所需成本很高。因此通常用可观测的替代变量来代替。本文不对真变量和替代变量间关系作任何模型假设,利用主要数据和核实数据,基于最小二乘方法和核方法,应用参数方法获得β的估计量,并证明了β的渐近正态性。

Consider linear models of the form Y=X^τβ＋e , where X is erroneously measured , and Y is measured exaotly . Many variables of intrest are difficult or expensive to be measured accurately and hence are usually replaced by surrogate variables. In this paper, without specifying any structure equations and distribution assumption of the true variable given the surrogate variable, a parametric method with the primary data is employed to obtain the estimator of β based the least-squared criterion and kernel method with the help of validation data. The asymptotic normality of the estiomator of β is derived.