Variable Error, Linear Regression Analysis

Consider linear models of the form Y = Xτβ+e , where the response variable Y is erroneously measured , and the p-variate explanatory X is measured exactly ,or where X is erroneously measured , and Y is measured exactly . Many variables of intrest are difficult or expensive to be measured accurately and hence are usually replaced by surrogate (?)ariables. 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.