Abstract: To deal with the region selection problem in functional linear models, we propose a functional information criterion that can be used to identify the null region where the functional predictor has no contribution to the response. The null region identified by our proposal is shown to be asymptotically consistent under some mild conditions. In addition, we obtain the convergence rate of the length of the null region estimate, which has not been considered previously. The procedure is easily implementable in practice. The finite-sample performance is illustrated in applications to simulated and real data.

Key words and phrases: functional data, information criterion, model selection, spline, support estimate, variable selection.