Locally sparse estimator for functional linear panel models with fixed effects

In this paper, we consider a locally sparse function linear panel model (LoS-FLPM), which investigates the impact of functional predictors on a scalar response when repeated measurements are available on multiple subjects. The coefficient function is assumed to be locally sparse, i.e., the function value is zero on some subregions of the domain. Employing fixed effects transformation, we propose a locally sparse estimator of coefficient function, and show its consistency and oracle property meaning the null and nonnull subregions can be identified with probability tending to one. Meanwhile, we present the asymptotic distribution of the estimator on nonnull subregions. The Monte Carlo simulation studies investigating the finite sample performance of the proposed methodology confirm our asymptotic results. A practical application is also considered.