On the asymptotic normality of frequency polygons for strongly mixing spatial processes

TL;DR

This paper proves that frequency polygons for stationary strongly mixing spatial processes are asymptotically normally distributed under minimal conditions, improving previous results in the field.

Contribution

It introduces a simplified method to establish asymptotic normality of frequency polygons with minimal bin width conditions for strongly mixing spatial processes.

Findings

Frequency polygons are asymptotically normal under minimal conditions.

The method simplifies previous proofs and relaxes conditions.

Improves upon earlier results by Carbon, Francq, and Tran (2010).

Abstract

This paper establishes the asymptotic normality of frequency polygons in the context of stationary strongly mixing random fields indexed by $\Z^d$. Our method allows us to consider only minimal conditions on the width bins and provides a simple criterion on the mixing coefficients. In particular, we improve in several directions a previous result by Carbon, Francq and Tran (2010).