Degrees of Freedom of the Lasso in Repeated Measurements Model

Abstract

First of all, we introduce the repeated measurements model and discuss the degrees of freedom of its coefficients in the structure of Stein's unbiased risk estimate (SURE). By assuming that the design matrix has full columns rank, the following results are concluded. First one, the number of non-zero coefficients is an unbiased estimate for degrees of freedom of lasso solution. Second one, the unbiased estimator of these non-zero coefficients is asymptotically consistent. In addition, It is concluded that the same above results will be obtained if there are no especial assumption on the design matrix. With all above results the optimal lasso solution can be obtained by using several model selection criteria such as ,  and   Moreover, -lasso shrinkage will be chosen if the variable selection is the main choice in applying lasso problem.