Regression with correlated predictors presents a challenging problem for parameter estimation and variable selection because highly correlated predictors are easy to cause the ill-posed problem of multicollinearity.In solving the ill-posed regression,ridge regression (Hoerl and Kennard,1970) and partial least square(PLS) are two important parameter estimation methods.But these methods dont set any coefficients to 0 and hence dont select important variables from all the predictors.Tibshirani (1996) proposes lasso based L1 penalty to obtain the sparse coefficients for variable selection.Efron et a1.(2004) propose LARS which can be used to obtain the paths of variables of lasso.