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Asymptotic results for hybrids of empirical and partial sums processes

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  • Sergio Alvarez-Andrade
  • Salim Bouzebda

Abstract

The present paper is devoted to the study of the hybrids of empirical and partial sums processes. In the first part, we present a synthesis of results related to these processes and their connection with the empirical and compound process. We obtain new results on the precise asymptotics in the law of the logarithm related to complete convergence and a.s. convergence, under some mild conditions, for the hybrids of empirical and partial sums processes. Finally, the weighted bootstrap processes and general hybrid processes are also discussed. Copyright Springer-Verlag Berlin Heidelberg 2014

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  • Sergio Alvarez-Andrade & Salim Bouzebda, 2014. "Asymptotic results for hybrids of empirical and partial sums processes," Statistical Papers, Springer, vol. 55(4), pages 1121-1143, November.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:4:p:1121-1143
    DOI: 10.1007/s00362-013-0557-3
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    References listed on IDEAS

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    1. Zhang, Yong & Yang, Xiao-Yun, 2008. "Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1051-1055, July.
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    4. Gut, Allan & Spataru, Aurel, 2003. "Precise asymptotics in some strong limit theorems for multidimensionally indexed random variables," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 398-422, August.
    5. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 2000. "Approximations for weighted bootstrap processes with an application," Statistics & Probability Letters, Elsevier, vol. 48(1), pages 59-70, May.
    6. Erich Haeusler & David M. Mason, 1999. "Weighted Approximations to Continuous Time Martingales with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 281-295, June.
    7. Jamel Jouini, 2010. "Bootstrap methods for single structural change tests: power versus corrected size and empirical illustration," Statistical Papers, Springer, vol. 51(1), pages 85-109, January.
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    Cited by:

    1. Nour-Eddine Berrahou & Salim Bouzebda & Lahcen Douge, 2024. "The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-37, June.

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