Joint data-driven estimation of impact-point number and locations

Develop a fully data-driven theory for simultaneously estimating both the number and the locations of point impacts in the spatial semi-functional linear regression model.

Background

The paper’s testing framework permits data-dependent and unobserved impact locations, but its asymptotic theory assumes that the number of impact points is fixed and that the estimated number is consistent, with the probability of correctly estimating it tending to one. The impact locations are likewise required to satisfy explicit rate conditions. A general theory that jointly treats data-driven selection of the number of impact points and estimation of their locations is therefore left unresolved.