Nonparametric M-Estimation for Functional Spatial Data

Abstract

This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we considerN be a F × R-valued measurable strictly stationary spatial process, where F is a semi-metric space and we study the spatial interaction of X i and Y i via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.

Asymptotic Normality of Nonparametric Kernel Regression Estimation for Missing at Random Functional Spatial Data

“…Te authors constructed the rates of almost sure convergence using the nonparametric kernel method in functional regression. Ten, the authors in [12] determined the asymptotic normality of robust regression simultaneously. We take note that the spatial functional regression is a particular case of two widely recognized spatial dependence models that have garnered signifcant interest in the analysis of lattice data, known as the spatial autoregressive (SAR)-dependent variable and the spatial autoregressive error (SAE), where the model error is SAR.…”