Adaptive LASSO in High-dimensions

The Least Absolute Shrinkage and Selector operator (LASSO) is a famous method for

estimation and predictor selection simultaneously. But in certain situations where the LASSO

is not consistent for predictor selection, Zou (2006). Therefore, he suggested a new type of the

LASSO, called the adaptive LASSO, where ordinary least squares estimators are used as weights

for penalizing dierent coecients in the

L

1

penalty. He proved that the adaptive LASSO

enjoys the oracle properties. But in high-dimensional data problems, (

p



n

), the weights for

adaptive LASSO is infeasible to calculated. Huang et al. (2008) have studied the asymptotic

properties of the adaptive Lasso estimators in sparse, high-dimensional linear regression models

under suitable conditions. Mainly, they assumed that under a partial orthogonality condition

in which the predictors with zero coecients are weakly correlated with the covariates with

nonzero coecients, marginal regression can be used to obtain the initial estimator. In this

article, this assumption is relax and used the ridge regression coecients as weights in the

L

1

penalty. In this scenario, it is also prove that the adaptive LASSO still has the oracle

property under given situations. Simulations and real data analysis are carried out to provide

prediction and variable selection performance of suggested techniqueThe Least Absolute Shrinkage and Selector operator (LASSO) is a famous method for

estimation and predictor selection simultaneously. But in certain situations where the LASSO

is not consistent for predictor selection, Zou (2006). Therefore, he suggested a new type of the

LASSO, called the adaptive LASSO, where ordinary least squares estimators are used as weights

for penalizing dierent coecients in the

L

1

penalty. He proved that the adaptive LASSO

enjoys the oracle properties. But in high-dimensional data problems, (

p



n

), the weights for

adaptive LASSO is infeasible to calculated. Huang et al. (2008) have studied the asymptotic

propertiesThe Least Absolute Shrinkage and Selector operator (LASSO) is a famous method for estimation and predictor selection simultaneously. But in certain situations where the LASSO is not consistent for predictor selection, Zou (2006). Therefore, he suggested a new type of the LASSO, called the adaptive LASSO, where ordinary least squares estimators are used as weights for penalizing dierent coecients in the L1 penalty. He proved that the adaptive LASSO enjoys the oracle properties. But in high-dimensional data problems, (p  n), the weights for adaptive LASSO is infeasible to calculated. Huang et al. (2008) have studied the asymptotic properties of the adaptive Lasso estimators in sparse, high-dimensional linear regression models under suitable conditions. Mainly, they assumed that under a partial orthogonality condition in which the predictors with zero coecients are weakly correlated with the covariates with nonzero coecients, marginal regression can be used to obtain the initial estimator. In this article, this assumption is relax and used the ridge regression coecients as weights in the L1􀀀penalty. In this scenario, it is also prove that the adaptive LASSO still has the oracle property under given situations. Simulations and real data analysis are carried out to provide prediction and variable selection performance of suggested technique. of the adaptive Lasso estimators in sparse, high-dimensional linear regression models

under suitable conditions. Mainly, they assumed that under a partial orthogonality condition

in which the predictors with zero coecients are weakly correlated with the covariates with

nonzero coecients, marginal regression can be used to obtain the initial estimator. In this

article, this assumption is relax and used the ridge regression coecients as weights in the

L

1

penalty. In this scenario, it is also prove that the adaptive LASSO still has the oracle

property under given situations. Simulations and real data analysis are carried out to provide

prediction and variable selection performance of suggested technique