AbstractWe consider sparse high-dimensional linear regression models. Penalized regressionshave been used as e ective methods for variable selection and estimation in high-dimensional models. In penalized regressions, it is common practice to standardizevariables before tting a penalized model and then t a penalized model with stan-dardized variables. Finally, the estimated coecients from a penalized model are re-covered to the scale on original variables. However, these procedures produce a slightlydi erent solution compared to the corresponding original penalized problem. In thispaper, we investigate issues on the standardization of variables in penalized regressionsand formulate the de nition of the standardized penalized estimator. In addition, wecompare the original penalized estimator with the standardized penalized estimatorthrough simulation studies and real data analysis.Keywords: LASSO, nonconvex penalties, penalized regression, standardization. 1. Introduction Consider the linear regression modely = X + ; (1.1)where y = (y