Variable selection in function-on-scalar single-index model via the alternating direction method of multipliers

We develop a new method for variable selection in a function-on-scalar single-index model. The proposed method goes beyond existing additive function-on-scalar regression framework and models dynamic effects of multiple scalar covariates via a varying coefficient single-index model. The unknown bivariate link function is modeled with splines. A computationally efficient alternating direction method of multipliers-based algorithm is used for simultaneous selection of the influential covariates and estimation of the single-index coefficients and the link function. The proposed method provides a flexible framework for variable selection in function-on-scalar regression, particularly in the presence of nonlinear and interaction effects. Numerical analysis using simulations illustrates satisfactory finite sample performance of the proposed method in terms of selection and estimation accuracy. An application is demonstrated on the CD4+ cell counts data. Software implementation of the proposed method is provided in R.