On the Consistency of Kernel Classification Rule for Functional Random Field

Résumé

We consider the classical moving window rule of classification for functional spatially dependent data. We investigate asymptotic properties of this nonparametric classification rule based on training data drawn from a or b-mixing random field taking values in infinite-dimensional space. We extend the results of Younso (2017) concerning both the consistency and the strong consistency of the moving window classifier to the spatially dependent case under mild assumptions. We propose a method for bandwidth selection and we conduct some simulation studies.