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Local robustness of sign tests in AR(1) against outliers

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Abstract

The paper deals with robustness of nonparametric sign tests against outliers in the autoregression AR(1) model. We consider the local scheme of data contamination by independent additive outliers with intensity O(n −1/2). The qualitative robustness of tests in terms of power equicontinuity is obtained.

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References

  1. T.W. Anderson, The Statistical Analysis of Time Series (Wiley, New York, 1971).

    MATH  Google Scholar 

  2. G. Boente, R. Fraiman, and V. J. Yohai, “Qualitative Robustness for Stochastic Processes”, Ann. Statist. 15, 1293–1312 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  3. M. V. Boldin and Yu. N. Tyurin, “On Nonparametric Sign Procedures in Autoregression Models”, Math. Methods Statist. 3, 279–305 (1994).

    MATH  MathSciNet  Google Scholar 

  4. M. V. Boldin, G. I. Simonova, and Yu. N. Tyurin, Sign-Based Methods in Linear Statistical Models (AMS, Providence, 1997).

    Google Scholar 

  5. M. V. Boldin and W. Stute, “On Sign Tests in ARMA Models with Possibly Infinite Error Variance”, Theory Probab. Appl. 49(3), 392–413 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  6. S. K. Dhar, “Minimum Distance Estimation in an Additive Effects Outliers Model”, Ann. Statist. 19(1), 205–228 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Hallin, J.-Fr. Ingenbleek, and M. L. Puri, “Linear Serial Rank Tests for Randomness Against ARMA Alternatives”, Ann. Statist. 13, 1156–1181 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Hallin, J.-Fr. Ingenbleek, and M. L. Puri, “Linear and Quadratic Rank Tests for Randomness Against Serial Dependence”, J. Time Ser. Anal. 8, 409–424 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Hallin and M. L. Puri, “Optimal Rank-Based Procedures for Time Series Analysis: Testing an ARMA Model against Other ARMA Models”, Ann. Statist. 16, 402–432 (1988).

    Article  MATH  MathSciNet  Google Scholar 

  10. M. Hallin and M. L. Puri, “Time Series Analysis via Rank Order Theory: Signed-Rank Tests for ARMA Models”, J. Multivariate Anal. 39, 1–29 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Hallin and M. L. Puri, “Aligned Rank Test for Linear Models with Autocorrelated Error Terms”, J. Multivariate Anal. 50, 175–237 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  12. F. R. Hampel, “A General Qualitative Definition of Robustness”, Ann. Math. Statist. 42, 1887–1896 (1971).

    Article  MATH  MathSciNet  Google Scholar 

  13. F. R. Hampel, E.M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel, Robust Statistics. The Approach Based on Influence Functions (Wiley, New York, 1986).

    MATH  Google Scholar 

  14. H. L. Koul, Weighted Empiricals and Linear Models (IMS, Hayward, 1992).

    MATH  Google Scholar 

  15. J. P. Kreiss, “On Adaptive Estimation in Stationary ARMA Processes”, Ann. Statist. 15, 112–133 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  16. R.D. Martin and V. J. Yohai, “Influence Functionals for Time Series”, Ann. Statist. 14, 781–818 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Rieder, “Qualitative Robustness of Rank Tests”, Ann. Statist. 10, 205–211 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  18. H. Rieder, “A Robust Asymptotic TestingModel”, Ann. Statist. 6, 1080–1094 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  19. H. Rieder, “Robustness of One- and Two-Sample Rank Tests Against Gross Errors”, Ann. Statist. 9, 245–265 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  20. H. Rieder, Neighborhoods as Nuisance Parameters? Robustness vs. Semiparametrics (New version). Discussion Paper No. 25, SFB 373 (Humboldt-Univ., Berlin, 2000).

    Google Scholar 

  21. A. A. Sorokin, Residual Empirical Processes in Statistical Analisis of Heteroscedastic Models, Ph.D. Thesis (Moscow State Univ., Moscow, 2007).

    Google Scholar 

  22. A. E. Vyazilov, “Empirical Processes and Robust Estimation of Parameters of the GARCH Model”, Math. Methods Statist. 12, 231–245 (2003).

    MathSciNet  Google Scholar 

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Correspondence to M. V. Boldin.

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Boldin, M.V. Local robustness of sign tests in AR(1) against outliers. Math. Meth. Stat. 20, 1–13 (2011). https://doi.org/10.3103/S1066530711010017

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  • DOI: https://doi.org/10.3103/S1066530711010017

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