Asymptotic normality of kernel estimates in a regression model for random fields

TL;DR

This paper proves the asymptotic normality of kernel regression estimators for dependent random fields, including martingale-difference and strongly mixing fields, and introduces a related statistical test for image analysis.

Contribution

It extends the asymptotic normality results to dependent random fields and proposes a new statistical test for image analysis applications.

Findings

Asymptotic normality established for kernel estimators in dependent fields

Applicable to martingale-difference and strongly mixing random fields

Introduces a statistical test for image analysis

Abstract

We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On this basis, a statistical test that can be applied to image analysis is also presented.