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Another look at the Tail Area Influence Function

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Abstract

A new way of computing the Tail Area Influence Function (TAIF) exactly is proposed and a new finite sample robustness measure, based on the TAIF, is introduced. The main properties of this robustness measure are also studied, for both finite and asymptotic sample sizes. Next, a very accurate approximation to the finite sample power function of a test is obtained; this is based on the TAIF plus an iterative procedure. The results are valid when there are no nuisance parameters.

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References

  • Field CA, Ronchetti EM (1985) A Tail Area Influence Function and its application to testing. Commun Stat 4: 19–41

    MATH  MathSciNet  Google Scholar 

  • García-Pérez A (1996) Behaviour of sign test and one sample median test against changes in the model. Kybernetika 32(2): 159–173

    MATH  MathSciNet  Google Scholar 

  • García-Pérez A (2003) Von Mises approximation of the critical value of a test. Test 12(2): 385–411

    Article  MATH  MathSciNet  Google Scholar 

  • García-Pérez A (2006a) Chi-Square tests under models close to the normal distribution. Metrika 63(3): 343–354

    Article  MATH  MathSciNet  Google Scholar 

  • García-Pérez A (2006b) T-tests with models close to the normal distribution. In: Balakrishnan N, Castillo E, Sarabia JM (eds) Advances in distribution theory, order statistics, and inference. Birkhäuser-Springer, Boston, pp 363–379

    Chapter  Google Scholar 

  • García-Pérez A (2008) Approximations for F-tests which are ratios of sums of squares of independent variables with a model close to the normal. Test 17(2): 350–369

    Article  MATH  MathSciNet  Google Scholar 

  • Laha RG, Rohatgi VK (1979) Probability theory. Wiley, New York

    MATH  Google Scholar 

  • Maronna RA, Martin RD, Yohai VJ (2006) Robust statistics: theory and methods. Wiley, New York

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Estadística, Investigación Operativa y Cálculo Numérico, Universidad Nacional de Educación a Distancia (UNED), Paseo Senda del Rey 9, 28040, Madrid, Spain

    A. García-Pérez

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  1. A. García-Pérez
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Correspondence to A. García-Pérez.

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García-Pérez, A. Another look at the Tail Area Influence Function. Metrika 73, 77–92 (2011). https://doi.org/10.1007/s00184-009-0266-z

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  • DOI: https://doi.org/10.1007/s00184-009-0266-z

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