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Asymptotic results for hybrids of empirical and partial sums processes

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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.

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Acknowledgments

The authors are grateful to the Editor-in-Chief, an Associate Editor and the two anonymous referees for thorough proofreading and numerous comments which led to a considerable improvement of the presentation.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Appliquées de Compiègne, Université de Technologie de Compiègne, B.P. 529, 60205 , Compiègne cedex, France

    Sergio Alvarez-Andrade & Salim Bouzebda

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  1. Sergio Alvarez-Andrade
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  2. Salim Bouzebda
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Correspondence to Salim Bouzebda.

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Alvarez-Andrade, S., Bouzebda, S. Asymptotic results for hybrids of empirical and partial sums processes. Stat Papers 55, 1121–1143 (2014). https://doi.org/10.1007/s00362-013-0557-3

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