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

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  • Mohamed El Machkouri

Abstract

This paper establishes the asymptotic normality of frequency polygons in the context of stationary strongly mixing random fields indexed by $$\mathbb {Z}^d$$ 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 . Copyright Springer Science+Business Media Dordrecht 2013

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  • Mohamed El Machkouri, 2013. "On the asymptotic normality of frequency polygons for strongly mixing spatial processes," Statistical Inference for Stochastic Processes, Springer, vol. 16(3), pages 193-206, October.
    • Handle: RePEc:spr:sistpr:v:16:y:2013:i:3:p:193-206
    DOI: 10.1007/s11203-013-9086-x
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    References listed on IDEAS

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    1. J. Beirlant & A. Berlinet & L. Györfi, 1999. "On piecewise linear density estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(3), pages 287-308, November.
    2. Carbon, Michel & Tran, Lanh Tat & Wu, Berlin, 1997. "Kernel density estimation for random fields (density estimation for random fields)," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 115-125, December.
    3. Marc Hallin & Zudi Lu & Lanh T. Tran, 2001. "Density estimation for spatial linear processes," ULB Institutional Repository 2013/2109, ULB -- Universite Libre de Bruxelles.
    4. Bosq, Denis & Merlevède, Florence & Peligrad, Magda, 1999. "Asymptotic Normality for Density Kernel Estimators in Discrete and Continuous Time," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 78-95, January.
    5. Tran, Lanh Tat, 1990. "Kernel density estimation on random fields," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 37-53, July.
    6. Mohamed El Machkouri, 2011. "Asymptotic normality of the Parzen–Rosenblatt density estimator for strongly mixing random fields," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 73-84, February.
    7. Carbon, Michel & Garel, Bernard & Tran, Lanh Tat, 1997. "Frequency polygons for weakly dependent processes," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 1-13, April.
    8. Marc Hallin & Michel Carbon & Lanh T. Tran, 1996. "Kernel density estimation on random fields: the L1 theory," ULB Institutional Repository 2013/2065, ULB -- Universite Libre de Bruxelles.
    9. Nadia Bensaïd & Sophie Dabo-Niang, 2010. "Frequency polygons for continuous random fields," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 55-80, April.
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