Statistical Analysis For Linear Regression Models With Additive Measurement Errors

When we deal with the measurement error data,the naive procedure by simply ignoring measurement errors always leads to a biased and inconsistent estimator.As a result,we should solve such practical problems by choosing relative measurement error models.There are two types of measurement error data.One has a multiplicative fashion,which we call distortion measurement error models.Another one is additive measurement error models.In this paper we consider the additive measurement error models.In this paper,we study a linear regression model where both the response and covariates can only be observed after being distorted by some additive factors.A residual based estimator is proposed.Then we establish the root n-consistency and asymptotic normality.To test a hypotheses on the parametric components,a test statistic based on the normalized difference between the residual sums of squares under the null and alternative hypotheses is proposed.We also employ the smoothly clipped absolute deviation penalty to select the relevant variables.The resulting penalized estimators are showed to be asymptotically normal and have the oracle property.Last,simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for an illustration.