Computational Statistics

, Volume 25, Issue 2, pp 269–289 | Cite as

A note on studentized confidence intervals for the change-point

  • Marie Hušková
  • Claudia KirchEmail author
Original Paper


We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. It is known how to construct resampling confidence intervals using blocking techniques, but so far no studentizing has been considered. A simulation study shows that we obtain better intervals by studentizing. When studentizing dependent data, we need to use flat-top kernels for the estimation of the asymptotic variance. It turns out that this estimator taking possible changes into account behaves much better than the corresponding Bartlett estimator. Since the asymptotic distribution of change-point statistics for time-series depends on this value, having a good estimator under the null as well as alternatives is also essential for testing problems.


Block bootstrap Mixing Flat-top kernel Change in mean 

Mathematics Subject Classification (2000)

62G09 62G15 60G10 


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Supplementary material

180_2009_175_MOESM1_ESM.pdf (15.6 mb)
ESM 1 (PDF 15,987 kb)
180_2009_175_MOESM2_ESM.pdf (22.6 mb)
ESM 2 (PDF 23,109 kb)


  1. Antoch J, Hušková M, Veraverbeke N (1995) Change-point problem and bootstrap. J Nonparametr Stat 5: 123–144zbMATHCrossRefGoogle Scholar
  2. Berkes I, Horváth L, Kokoszka P, Shao Q-M (2005) Almost sure convergence of the Bartlett estimator. Period Math Hungar 51: 11–25zbMATHCrossRefMathSciNetGoogle Scholar
  3. Götze F, Künsch HR (1996) Second-order correctness of the blockwise bootstrap for stationary observations. Ann Stat 24: 1914–1933zbMATHCrossRefGoogle Scholar
  4. Hušková M (2004) Permutation principle and bootstrap in change point analysis. Fields Inst Commun 44: 273–291Google Scholar
  5. Hušková M, Kirch C (2008) Bootstrapping confidence intervals for the change-point of time series. J Time Ser Anal 27: 330–349Google Scholar
  6. Kirch C (2006) Resampling methods for the change analysis of dependent data. PhD Thesis, University of Cologne, Cologne, 2006.
  7. Kirch C (2007) Block permutation principles for the change analysis of dependent data. J Stat Plann Inference 137: 2453–2474zbMATHCrossRefMathSciNetGoogle Scholar
  8. Politis DN (2003) Adaptive bandwidth choice. J Nonparametr Stat 15: 517–533zbMATHCrossRefMathSciNetGoogle Scholar
  9. Politis DN, Romano JP (1995) Bias-corrected nonparametric spectral estimation. J Time Ser Anal 16: 67–103zbMATHCrossRefMathSciNetGoogle Scholar
  10. Shorack GR, Wellner JA (1986) Empirical processes with applications to statistics. Wiley, New YorkzbMATHGoogle Scholar
  11. Silverman BW (1986) Density estimation. Chapman and Hall, LondonzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of StatisticsCharles University of PraguePraha 8Czech Republic
  2. 2.Institute for StochasticsKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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