Journal of Time Series Analysis

Bootstrapping Robust Statistics for Markovian Data Applications to Regenerative R ‐Statistics and L ‐Statistics

Journal Article

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

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.