On the local linear estimation of a generalized regression function with spatial functional data

Abstract

This paper focuses on non parametric estimator regression of scalar response variable given a functional variable when the observations are spatially dependent by local linear method. Then, under some general conditions, in terms of the uniform almost complete convergence with rate of this estimator is treated. Moreover, the usefulness of our results is illustrated through their application to climatological data.

Keywords:

• Spatial functional data
• local linear estimation
• non parametric estimator regression
• rate of convergence
• strongly mixing process

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G20
• 62H11

Notes

1 Let $\mathcal{S}$ be a subset of a semimetric space $\mathcal{F},$ and let $ϵ>0$ be given. A finite set of points $x_1,x_2,\dots ,x_N$ in $\mathcal{F}$ is called an ϵ-net for $\mathcal{S}$ if $\mathcal{S}\subset {\cup }_{k=1}^{N}B(x_k,ϵ).$ The quantity ${\psi }_{\mathcal{S}}(ϵ)=ln(N_{ϵ}(\mathcal{S})),$ where $N_{ϵ}(\mathcal{S})$ is the minimal number of open balls in $\mathcal{F}$ of radius ϵ which is necessary to cover $\mathcal{S},$ is called Kolmogorov’s ϵ-entropy of the set $\mathcal{S}.$