Pairwise fusion approach incorporating prior constraint information (Q1988277)

The authors consider a linear regression model under convex prior constraints and under sparsity as well as homogeneity conditions. Sparsity means that only a small fraction of regression coefficients is nonzero, and homogeneity means that regression coefficients are grouped and have exactly the same value in each group. The associated estimation problem requires the constrained minimization of an objective function which has additional to the least squares part also penalized sparsity and homogeneity parts. The authors propose a pairwise fusion approach. The minimization problem is solved by an alternating direction method of multipliers (ADMM). The convergence of the algorithm as well as asymptotic properties of the estimator are proved. The paper is finished with simulation studies and a real data example.