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Data driven rank test for the change point problem

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Abstract

Data driven test procedure for detection of change is introduced and its properties are studied. The new solution is max-type statistic related to data-driven rank tests for two-sample subproblems. Simulations show that the new test possesses high and stable power. The test is consistent at essentially any alternative. Asymptotic null distribution of the test is derived.

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References

  • Antoch J, Hušková M, Jarušková D (2002) Off-line quality control. In: Lauro NC et al (eds) Multivariate total quality control: foundation and recent advances. Springer, Heidelberg, pp 1–86

    Google Scholar 

  • Chambers JM, Mallows CL, Stuck BW (1976) A method for simulating stable random variables. J Am Stat Assoc 71:340–344

    Article  MathSciNet  MATH  Google Scholar 

  • Csörgő M, Horváth L (1988) Nonparametric methods for change point problems. In: Krishnaiah PR, Rao CR (eds) Handbook of statistics, vol 7. Elsevier, Amsterdam, pp 403–425

    Google Scholar 

  • Csörgő M, Horváth L (1997) Limit theorems in change-point analysis. Wiley, New York

    Google Scholar 

  • DeLong DM (1981) Crossing probabilities for square root boundary by a Bessel process. Commun Stat Theory Meth 10:2197–2213

    Article  MathSciNet  Google Scholar 

  • Ducharme GR, Ledwina T (2003) Efficient and adaptive nonparametric test for the two-sample problem. Ann Stat 31:2036–2058

    Article  MathSciNet  MATH  Google Scholar 

  • Fan J (1996) Test of significance based on wavelet thresholding and Neyman’s truncation. J Am Stat Assoc 91:674–688

    Article  MATH  Google Scholar 

  • Haughton D, Haughton J, Izenman AJ (1990) Information criteria and harmonic models in time series analysis. J Stat Comput Simul 35:187–207

    Article  MathSciNet  Google Scholar 

  • Hušková M (1997) Limit theorems for rank statistics. Stat Prob Lett 32:45–55

    Article  MATH  Google Scholar 

  • Hušková M, Sen PK (1989) Nonparametric tests for shift and change in regression at an unknown time point. In: Hackl P (ed) Statistical analysis and forecasting of economic structural change. Springer, Berlin, pp 71–85

    Google Scholar 

  • Janic-Wróblewska A, Ledwina T (1997) Data driven rank test for two-sample problem. Technical Report No. 3/97, Institute of Mathematics, Wrocław University of Technology

  • Janic-Wróblewska A, Ledwina T (2000) Data driven rank test for two-sample problem. Scand J Stat 27:281–297

    Article  MATH  Google Scholar 

  • Neuhaus G (1987) Local asymptotics for linear rank statistics with estimated score functions. Ann Stat 15:491–512

    Article  MathSciNet  MATH  Google Scholar 

  • Praagman J (1986) Efficiency of change-point tests. Dissertation, University of Eindhoven, The Netherlands

  • Shorack GR, Wellner JA (1986) Empirical processes with applications to statistics. Wiley, New York

    Google Scholar 

  • Yao Y-C (1990) On asymptotic behavior of a class of nonparametric tests. Stat Prob Lett 9:173–177

    Article  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Statistics, Charles University, Sokolovská 83, 186 00, Praha, Czech Republic

    Jaromír Antoch & Marie Hušková

  2. Institute of Mathematics and Informatics, Wroclaw University of Technology, Wyb. Wyspiańskiego 27, 50-370, Wrocław, Poland

    Alicja Janic

  3. Institute of Mathematics, Polish Academy of Sciences, ul. Kopernika 18, 51-617, Wrocław, Poland

    Teresa Ledwina

Authors
  1. Jaromír Antoch
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  2. Marie Hušková
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  3. Alicja Janic
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  4. Teresa Ledwina
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Corresponding author

Correspondence to Marie Hušková.

Additional information

The work of the first two authors has been partially supported by the grants GAČR 201/06/0186 and MSM 02160839.

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Antoch, J., Hušková, M., Janic, A. et al. Data driven rank test for the change point problem. Metrika 68, 1–15 (2008). https://doi.org/10.1007/s00184-007-0139-2

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  • DOI: https://doi.org/10.1007/s00184-007-0139-2

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