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Bootstrapping Not Independent and Not Identically Distributed Data

Author

Listed:
  • Martin Hrba

    (Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 49/83, 18675 Prague, Czech Republic)

  • Matúš Maciak

    (Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 49/83, 18675 Prague, Czech Republic)

  • Barbora Peštová

    (Department of Statistical Modelling, Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou věží 271/2, 18207 Prague, Czech Republic)

  • Michal Pešta

    (Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Sokolovská 49/83, 18675 Prague, Czech Republic)

Abstract

Classical normal asymptotics could bring serious pitfalls in statistical inference, because some parameters appearing in the limit distributions are unknown and, moreover, complicated to estimated (from a theoretical as well as computational point of view). Due to this, plenty of stochastic approaches for constructing confidence intervals and testing hypotheses cannot be directly applied. Bootstrap seems to be a plausible alternative. A methodological framework for bootstrapping not independent and not identically distributed data is presented together with theoretical justification of the proposed procedures. Among others, bootstrap laws of large numbers and central limit theorems are provided. The developed methods are utilized in insurance and psychometry.

Suggested Citation

  • Martin Hrba & Matúš Maciak & Barbora Peštová & Michal Pešta, 2022. "Bootstrapping Not Independent and Not Identically Distributed Data," Mathematics, MDPI, vol. 10(24), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4671-:d:998884
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    References listed on IDEAS

    as
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