  This paper considers a high dimensional linear regression model with
corrected variables. A variety of methods have been developed in recent years,
yet it is still challenging to keep accurate estimation when there are complex
correlation structures among predictors and the response. We propose an
adaptive and "reversed" penalty for regularization to solve this problem. This
penalty doesn't shrink variables but focuses on removing the shrinkage bias and
encouraging grouping effect. Combining the l_1 penalty and the Minimax Concave
Penalty (MCP), we propose two methods called Smooth Adjustment for Correlated
Effects (SACE) and Generalized Smooth Adjustment for Correlated Effects
(GSACE). Compared with the traditional adaptive estimator, the proposed methods
have less influence from the initial estimator and can reduce the false
negatives of the initial estimation. The proposed methods can be seen as linear
functions of the new penalty's tuning parameter, and are shown to estimate the
coefficients accurately in both extremely highly correlated variables situation
and weakly correlated variables situation. Under mild regularity conditions we
prove that the methods satisfy certain oracle property. We show by simulations
and applications that the proposed methods often outperforms other methods.
