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On Bahadur–Kiefer Type Processes for Sums and Renewals in Dependent Cases

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Abstract

We study the asymptotic behavior of Bahadur–Kiefer processes that are generated by summing partial sums of (weakly or strongly dependent) random variables and their renewals. Known results for i.i.d. case will be extended to dependent cases.

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Acknowledgments

We wish to thank two referees for their careful reading of, and constructive remarks on, our manuscript. Research supported by an NSERC Canada Discovery Grant at Carleton University, Ottawa and by the Hungarian National Foundation for Scientific Research, No. K108615.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O.Box 127, Budapest, 1364, Hungary

    Endre Csáki

  2. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada

    Miklós Csörgő

Authors
  1. Endre Csáki
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  2. Miklós Csörgő
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Correspondence to Endre Csáki .

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Editors and Affiliations

  1. European Centre for Advanced Research in Economics and Statistics, Université Libre de Bruxelles, Bruxelles, Belgium

    Marc Hallin

  2. Department of Applied Economics and Statistics, University of Delaware, Newark, Delaware, USA

    David M. Mason

  3. School of Mathematics and Science, Carl von Ossietzky University, Oldenburg, Germany

    Dietmar Pfeifer

  4. Mathematical Institute, University of Cologne, Köln, Germany

    Josef G. Steinebach

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Csáki, E., Csörgő, M. (2015). On Bahadur–Kiefer Type Processes for Sums and Renewals in Dependent Cases. In: Hallin, M., Mason, D., Pfeifer, D., Steinebach, J. (eds) Mathematical Statistics and Limit Theorems. Springer, Cham. https://doi.org/10.1007/978-3-319-12442-1_6

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