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Recent developments in bootstrap methods for dependent data

Author

Listed:
  • Giuseppe Cavaliere
  • Dimitris N. Politis
  • Anders Rahbek
  • Patrice Bertail
  • Stéphan Clémençon
  • Jessica Tressou

Abstract

type="main" xml:id="jtsa12105-abs-0001"> This article is devoted to extending the notion of robustness in the context of Markovian data, based on their (pseudo-)regenerative properties and by studying its impact on the regenerative block-bootstrap (RBB). Precisely, it is shown how to possibly define the ‘influence function’ in this framework, so as to measure the impact of (pseudo-)regeneration data blocks on the statistic of interest. We also define the concept of regeneration-based signed linear rank statistic and L-statistic, as specific functionals of the regeneration blocks, which can be made robust against outliers in this sense. The asymptotic validity of the approximate RBB (ARBB), is established here, when applied to such statistics. For illustration purpose, we compare (A)RBB confidence intervals for the mean, the median and some L-statistics related to the (supposedly existing) stationary probability distribution μ(dx) of the chain observed and for their robustified versions as well. Copyright © 2015 Wiley Publishing Ltd

Suggested Citation

  • Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Patrice Bertail & Stéphan Clémençon & Jessica Tressou, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 462-480, May.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:3:p:462-480
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    File URL: http://hdl.handle.net/10.1111/jtsa.12105
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    Cited by:

    1. Germán Aneiros & Paula Raña & Philippe Vieu & Juan Vilar, 2018. "Bootstrap in semi-functional partial linear regression under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 659-679, September.

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