A method for variable selection in a multivariate functional linear regression model with multiple scalar responses

In this paper, we propose a new functional variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This procedure takes into account the loss incurred by selecting a subset of variables, measured by a criterion depending on this subset and involving covariance matrices of variables obtained from basis expansions of the initial functional predictors. By sorting in decreasing order the values of this criterion on the subsets obtained by removing each predictor, the set of relevant predictors is expressed as depending on two parameters which then need to be estimated. Estimates of these parameters based on appropriate penalizations of estimates of the criterion are then introduced, thereby leading to our proposal for variable selection. Simulation studies are carried out to evaluate the finite sample performance of the proposed method with comparison to that of several existing methods, and also a weather data set is analyzed.