In this paper, we propose least absolute shrinkage and selection operator (LASSO) estimators in semiparametric linear measurement error models when prior information for the parameters is available. When it is suspected that the parameter vector may be the null vector with some degree of uncertainty, we define improved LASSO estimators, which include the preliminary test LASSO estimator, the Stein-type LASSO estimator, and the positive-rule Stein-type LASSO estimator. The asymptotic properties of resulting estimators such as the asymptotic distributional quadratic biases and the asymptotic distributional quadratic risks are examined. For numerical analysis, we used relative efficiency and mean prediction error to compare the estimators. The shrinkage estimators showed better performance compared to the LASSO. Finally, the Egyptian pottery data set is analyzed.