Variable selection in multivariate linear models for functional data via sparse regularization

摘要

We consider the use of sparse regularization for the problem of variable selection in multivariate linear models where the predictors are given as functions and the responses are scalars. Observations corresponding to the predictors are assumed to be measured repeatedly at discrete time points, and, therefore, they are treated as smooth functional data. Parameters included in the functional multivariate linear model are estimated by the penalized least squares method with an ℓ_1/ℓ_2-type penalty. We construct a blockwise descent algorithm for deriving the estimates of the functional multivariate linear model. We also provide a model selection criterion for evaluating the model. To investigate the effectiveness of the proposed method, we apply it to the analysis of simulated data and real data.