Bootstrapping Not Independent and Not Identically Distributed Data

Martin Hrba, Matúš Maciak, Barbora Peštová and Michal Pešta ()
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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

Mathematics, 2022, vol. 10, issue 24, 1-26

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.

Keywords: bootstrap; statistical inference; asymptotic normality; weakly dependent data; not identically distributed data; moving block bootstrap; law of large numbers; central limit theorem; psychometric evaluation; non-life insurance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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