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

Abstract

This paper establishes the asymptotic normality of frequency polygons in the context of stationary strongly mixing random fields indexed by ${\mathbb{Z}}^d$. 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).