Variables Selection Methods On Collinearity In High-dimensional Linear Model

Variables selection plays a pivotal role in the contemporary statistical learn-ing and practical backgrounds.For collinearity, ordinary least square regression tends to be inefficient.Some dimension reduction methods are introduced,such as penalized likelihood ridge estimator,bridge estimator,principal component re-gression,partial least square regression and high-dimensional variables selection method elastic net method.By giving a new explaination on ridge penalty,we add the weight to l2 penalty of elastic net method and two kinds of weight selection methods are proposed.The real data performance and numerical stimulations in-dicate that mean prediction error on the weighted elastic net can be improved.