Locally sparse functional regression with an application to mortality data

A novel method for functional regression with functional response and functional covariate is discussed. The method is particularly useful when the regression surface is non-zero only on a subset of its bivariate domain, allowing for a local relation between the response and predictor variable. By means of a tensor product splines representation of the unknown functional coefficient and an overlap group lasso penalty we are able to effectively estimate the regression function. The model performance is illustrated through its application to the well-known Swedish Mortality dataset, clearly showing the local nature of the relation between the mortality at consecutive years.