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Asymptotic normality of recursive estimators under strong mixing conditions

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  • Aboubacar Amiri

Abstract

Dans ce papier, nous nous intéressons à l’estimation de la fonction de régression par une approche non-paramétrique par noyau. Nous établissons la normalité asymptotique, pour une famille générale d’estimateurs récursifs à noyau de la fonction de régression, sous une hypothèse de forte mélangence. Notre rsultat généralise ainsi le résulttat de Roussas and Tran (Ann Stat 20:98–120, 1992 ) sur l’estimateur de Devroye–Wagner. Copyright Springer Science+Business Media Dordrecht 2013

Suggested Citation

  • Aboubacar Amiri, 2013. "Asymptotic normality of recursive estimators under strong mixing conditions," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 81-96, July.
    • Handle: RePEc:spr:sistpr:v:16:y:2013:i:2:p:81-96
    DOI: 10.1007/s11203-013-9078-x
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    References listed on IDEAS

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    1. Harro Walk, 2001. "Strong Universal Pointwise Consistency of Recursive Regression Estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 691-707, December.
    2. Greblicki, Wlodzimierz & Pawlak, Miroslaw, 1987. "Necessary and sufficient consistency conditions for a recursive kernel regression estimate," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 67-76, October.
    3. Aboubacar Amiri, 2012. "Recursive regression estimators with application to nonparametric prediction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 169-186.
    4. Li Wang & Han-Ying Liang, 2004. "Strong uniform convergence of the recursive regression estimator under φ-mixing conditions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(3), pages 245-261, June.
    5. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
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