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A modified signed likelihood ratio test in elliptical structural models

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Abstract

In this paper we deal with the issue of performing accurate testing inference on a scalar parameter of interest in structural errors-in-variables models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as special case. We derive a modified signed likelihood ratio statistic that follows a standard normal distribution with a high degree of accuracy. Our Monte Carlo results show that the modified test is much less size distorted than its unmodified counterpart. An application is presented.

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References

  • Aoki, R., Bolfarine, H., Singer, J.M.: Null intercept measurement error regression models. Test 10, 441–457 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  • Arellano-Valle, R.B., Bolfarine, H.: Elliptical structural models. Commun. Stat. Theory Methods 25, 2319–2341 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O.E.: Inference on full or partial parameters, based on the standardized signed log likelihood ratio. Biometrika 73, 307–322 (1986)

    MATH  MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O.E.: Modified signed log likelihood ratio. Biometrika 78, 557–563 (1991)

    Article  MathSciNet  Google Scholar 

  • Barndorff-Nielsen, O.E., Blaesild, P., Eriksen, P.S.: Decomposition and Invariance of Measures, and Statistical Transformation Models. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  • Chan, L.K., Mak, T.K.: On the maximum likelihood estimation of a linear structural relationship when the intercept is known. J. Multivar. Anal. 9, 304–313 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  • Cheng, C.L., Van Ness, J.W.: Statistical Regression with Measurement Error. Oxford University Press, London (1999)

    MATH  Google Scholar 

  • Doornik, J.A.: Ox: An Object-Oriented Matrix Language. Timberlake Consultants Press, London (2006)

    Google Scholar 

  • Fang, K.T., Anderson, T.W.: Statistical Inference in Elliptically Contoured and Related Distributions. Allerton Press Inc, New York (1990)

    MATH  Google Scholar 

  • Fang, K.T., Kotz, S., Ng, K.W.: Symmetric Multivariate and Related Distributions. Chapman and Hall, London (1990)

    MATH  Google Scholar 

  • Fuller, S.: Measurement Error Models. Wiley, New York (1987)

    Book  MATH  Google Scholar 

  • Kelly, G.: The influence function in the errors in variables problem. Ann. Stat. 12, 87–100 (1984)

    Article  MATH  Google Scholar 

  • Pace, L., Salvan, A.: Principles of Statistical Inference from a Neo-Fisherian Perspective. World Scientific, Singapore (1997)

    MATH  Google Scholar 

  • Severini, T.A.: Likelihood Methods in Statistics. Oxford University Press, London (2000)

    MATH  Google Scholar 

  • Wong, M.Y.: Likelihood estimation of a simple linear regression model when both variables have error. Biometrika 76, 141–148 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  • Wong, M.Y.: Bartlett adjustment to the likelihood ratio statistic for testing several slopes. Biometrika 78, 221–224 (1991)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade Federal de Goiás, Campus Samambaia, CP 131, Goiânia, GO, 74001-970, Brazil

    Tatiane F. N. Melo

  2. Departamento de Estatística, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, 05508-090, Brazil

    Silvia L. P. Ferrari

Authors
  1. Tatiane F. N. Melo
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  2. Silvia L. P. Ferrari
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Correspondence to Tatiane F. N. Melo.

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Melo, T.F.N., Ferrari, S.L.P. A modified signed likelihood ratio test in elliptical structural models. AStA Adv Stat Anal 94, 75–87 (2010). https://doi.org/10.1007/s10182-010-0123-4

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  • DOI: https://doi.org/10.1007/s10182-010-0123-4

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