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

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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.

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Acknowledgments

The author thanks an anonymous referee for his\(\backslash \)her careful reading and constructive comments.

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  1. Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Université de Rouen, Avenue de l’Université, Technopôle du Madrillet, 76801 , Saint-Etienne du Rouvray, France

    Mohamed El Machkouri

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  1. Mohamed El Machkouri
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Correspondence to Mohamed El Machkouri.

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El Machkouri, M. On the asymptotic normality of frequency polygons for strongly mixing spatial processes. Stat Inference Stoch Process 16, 193–206 (2013). https://doi.org/10.1007/s11203-013-9086-x

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  • DOI: https://doi.org/10.1007/s11203-013-9086-x

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