<Para ID="Par1">The kernel method estimator of the spatial modal regression for functional regressors is proposed. We establish, under some general mixing conditions, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$L^p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>L</mi> <mi>p</mi> </msup> </math> </EquationSource> </InlineEquation>-consistency and the asymptotic normality of the estimator. The performance of the proposed estimator is illustrated in a...</equationsource></equationsource></inlineequation></para>

Let (Zi=(Xi,Yi),i∈ZN) be a F×R-valued measurable strictly stationary spatial process, where F is a semi-metric space. We study a kernel estimator of the conditional mode of the univariate response variable Yi given the functional variable Xi. The main aim of this paper is to prove the almost...