Asymptotic properties of the kernel estimate of spatial conditional mode when the regressor is functional

The kernel method estimator of the spatial modal regression for functional regressors is proposed. We establish, under some general mixing conditions, the $$L^p$$ L p -consistency and the asymptotic normality of the estimator. The performance of the proposed estimator is illustrated in a real data application. Copyright Springer-Verlag Berlin Heidelberg 2015