Adaptive and reversed penalty for analysis of high-dimensional correlated data

• Adaptive and “reversed” penalty which focuses on removing the shrinking bias and encouraging the grouping effect. • The proposed estimator obtains valid information even from the wrong initial estimates. • Provide stable and accurate estimation from finite samples in the setting that the predictors are highly correlated. Many large-scale applications of regression models have correlated data. Although a variety of methods have been developed for this modeling problem, yet it is still challenging to keep an accurate estimation. We propose an adaptive and “reversed” penalty, which focuses on removing the shrinking bias and encouraging the grouping effect. Combining the L 1 penalty and the Minimax Concave Penalty, we propose two methods called Smooth Adjustment for Correlated Effects and Generalized Smooth Adjustment for Correlated Effects. They can be seen as special adaptive estimators, but different from the traditional adaptive estimators that highly rely on the initial estimation. The proposed estimators obtain valid information even from the wrong initial estimates, providing stable and accurate estimation from finite samples. Under mild regularity conditions , we prove that the methods satisfy oracle property . Simulations show that the proposed procedures estimate the coefficients accurately in correlation structures. We also apply the proposed estimator to financial data and show that it is successful in asset allocation selection.