Mathematical Sciences

In practice, measurement error in the covariates is often encountered. Measurement error has several effects when using ordinary least squares for the regression problems. In this thesis, we introduce the basic idea of correcting the bias caused by different types of measurement error. We then focus on the variable selection for partially linear models when some of the covariates are measured with additive errors. The bias caused by the measurement error is corrected by subtracting a bias correction term in the squared loss function. Adaptive LASSO is used for the variable selection procedure. The rate of convergence and the asymptotic normality of the estimators resulted by the proposed procedure are established. We also proved that, with the correct choice of the rate of the regularization parameter, the proposed procedure asymptotically performs as well as when the true model is known in advance. This is the so-called oracle properties. ii Dedication I dedicate this work to my beloved parents. ii