Kernel deconvolution estimation for random fields

TL;DR

This paper proves the asymptotic normality of a kernel deconvolution estimator for strongly mixing random fields under minimal conditions, using Lindeberg's method instead of traditional coupling techniques.

Contribution

It introduces a new proof approach for asymptotic normality of kernel estimators in spatial processes, accommodating both mixing and certain nonmixing fields.

Findings

Asymptotic normality established under minimal bandwidth conditions

Applicable to both mixing and certain nonmixing random fields

Provides a new methodological approach using Lindeberg's method

Abstract

In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the strong mixing coefficients is provided. Our approach is based on the Lindeberg's method rather than on Bernstein's technique and coupling arguments widely used in previous works on nonparametric estimation for spatial processes. We deal also with nonmixing random fields which can be written as a (nonlinear) functional of i.i.d. random fields by considering the physical dependence measure coefficients introduced by Wu (2005).