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Chi-Square Tests Under Models Close to the Normal Distribution

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Abstract

Many test statistics follow a χ2 distribution because a normal model is assumed as underlying distribution. In this paper we obtain good analytic approximations for the p-value and the critical value of χ2 tests when the underlying distribution is close but different from the normal model. With these approximations we study the robustness of validity of χ2 tests

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References

  • Altman DG (1991) Practical statistics for medical research. Chapman and Hall, London

    Google Scholar 

  • Becker RA, Chambers JM, Wilks AR (1988) The new s language. Chapman and Hall, London (Formely Wadsworth and Brooks-Cole)

    MATH  Google Scholar 

  • Benjamini Y (1983) Is the t test really conservative when the parent distribution is long-tailed?. J Am Stat Assoc 78:645–654

    Article  MathSciNet  MATH  Google Scholar 

  • Box GEP (1953) Non-normality and tests on variances. Biometrika 40:318–335

    MathSciNet  MATH  Google Scholar 

  • Daniels HE (1983) Saddlepoint approximations for estimating equations. Biometrika 70:89–96

    Article  MathSciNet  MATH  Google Scholar 

  • Field CA, Ronchetti E (1985) A tail area influence function and its application to testing. Commun Stat 4:19–41

    MathSciNet  MATH  Google Scholar 

  • Filippova AA (1961) Mises’ theorem on the asymptotic behaviour of functionals of empirical distribution functions and its statistical applications. Theory Probab Appl 7:24–57

    Article  Google Scholar 

  • García-Pérez A (1993) On robustness for hypotheses testing. Int Stat Rev 61:369–385

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Hampel F (1974) The influence curve and its role in robust estimation. J Am Stat Assoc 69:383–393

    Article  MathSciNet  MATH  Google Scholar 

  • Jensen JL (1995) Saddlepoint approximations. Clarendon Press, Oxford

    Google Scholar 

  • Loh WY (1984) Bounds on AREs for restricted classes of distributions defined via tail-orderings. Ann Stat 12:685-701

    Article  MathSciNet  MATH  Google Scholar 

  • Lugannani R, Rice S (1980) Saddle point approximation for the distribution of the sum of independent random variables. Adv Appl Probab 12:475–490

    Article  MathSciNet  MATH  Google Scholar 

  • R Development Core Team (2003) The R Enviroment for statistical computing and graphics

  • Reeds JA (1976) On the definitions of von Mises functionals. PhD thesis, Harvard University, Cambridge, Massachusetts

    Google Scholar 

  • Rivest L-P (1986) Bartlett’s, Cochran’s, and Hartley’s tests on variances are liberal when the underlying distribution is long-tailed. J Am Stat Assoc 81:124–128

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Estadística, Investigación Operativa y Cálculo Numérico Facultad de Ciencias, U.N.E.D. 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. Chi-Square Tests Under Models Close to the Normal Distribution. Metrika 63, 343–354 (2006). https://doi.org/10.1007/s00184-005-0024-9

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  • DOI: https://doi.org/10.1007/s00184-005-0024-9

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