Advertisement

Classical and Bayesian Goodness-of-fit Tests for the Exponential Model: A Comparative Study

  • Maria J. Polidoro
  • Fernando J. Magalhães
  • Maria A. Amaral Turkman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8581)

Abstract

Most common statistical methodologies assume a parametric model for the data and inference is made based on that assumption. If the model does not fit the data, the resulting inference will be mislead. Thus, evaluation of the fitting of a proposed parametric statistical model to a given dataset becomes an important issue.

In several practical situations, namely in reliability and life sciences problems, the exponential model has been widely used and several classical tests were already proposed for its fitting evaluation. In this work we suggest two Bayesian tests when an exponential model is proposed to describe the data, and using a simulation study, we compare their power with the classical ones.

Keywords

Goodness-of-fit test Bayesian nonparametric model Bayes factor mixture of finite Polya trees power of test 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D’Agostino, R.B., Stephens, M.A.: Goodness-of-fit Techniques. Marcel Dekker, New York (1986)zbMATHGoogle Scholar
  2. 2.
    Baringhaus, L., Henze, N.: A class of consistent tests for exponentiality based on the empirical Laplace transform. Ann. Inst. Statist. Math. 43, 551–564 (1991)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Baringhaus, L., Henze, N.: Tests of fit for exponentiality based on a characterization via the mean residual life function. Statist. Paper 41, 225–236 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    Choi, B., Kim, K., Song, S.H.: Goodness of fit test for exponentiality based on Kullback-Leibler information. Comm. Statist. Simulation Comput. 33(2), 525–536 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Henze, N., Meintanis, S.: Recent and classical tests for exponentiality: A partial review with comparisons. Metrika 61, 29–45 (2005)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Grané, A., Fortiana, J.: A directional test of exponentiality based on maximum correlations. Metrika 73, 255–274 (2011)CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Gelman, A., Meng, X.L., Stern, H.: Posterior predictive assesssment of model fitness via realized discrepancies (with discussion). Statist. Sinica 6, 733–807 (1996)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Robins, J.M., Vaart, A., van der Ventura, V.: Asymptotic distribution of p-values in composite null models. J. Amer. Statist. Assoc. 95, 1143–1159 (2000)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Bayarri, M.J., Berger, J.O.: P-values for composite null models. J. Amer. Statist. Assoc. 95, 1127–1142 (2000)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Hjort, N.L., Dahl, F.A., Steinbakk, G.H.: Post-processing posterior predictive p-values. J. Amer. Statist. Assoc. 101, 1157–1174 (2006)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Johnson, V.E.: A Bayesian chi-squared test for goodness-of-fit. Ann. Statist. 32(6), 2361–2384 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  12. 12.
    Johnson, V.E.: Bayesian model assessment using pivotal quantities. Bayesian Analysis 2, 719–734 (2007)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Hjort, N.L., Holmes, C., Müller, P., Walker, S.G.: Bayesian Nonparametrics. Cambridge University Press, New York (2010)CrossRefzbMATHGoogle Scholar
  14. 14.
    Verdinelli, I., Wasserman, L.: Bayesian goodness-of-fit testing using infinite-dimensional exponential families. Ann. Statist. 26, 1215–1241 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  15. 15.
    Berger, J.O., Guglielmi, A.: Bayesian and conditional frequentist testing of a parametric model versus nonparametric alternatives. J. Amer. Statist. Assoc. 96, 174–184 (2001)CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    Tokdar, S.T., Martin, R.: Bayesian test of normality versus a Dirichlet process mixture alternative. ArXiv e-prints (2011)Google Scholar
  17. 17.
    Lavine, M.: Some aspects of Polya tree distributions for statistical modeling. Ann. Statist. 20, 1222–1235 (1992)CrossRefMathSciNetzbMATHGoogle Scholar
  18. 18.
    Lavine, M.: More aspects of Polya tree distributions for statistical modeling. Ann. Statist. 22, 1161–1176 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    Hanson, T., Johnson, W.: Modeling regression errors with a mixture of Polya trees. J. Amer. Statist. Assoc. 97, 1020–1033 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    Hanson, T.: Inference for mixture of finite Polya tree models. J. Amer. Statist. Assoc. 101, 1548–1565 (2006)CrossRefMathSciNetzbMATHGoogle Scholar
  21. 21.
    Schervish, M.J.: Theory os Statistic. Springer, New York (1995)CrossRefGoogle Scholar
  22. 22.
    Cox, D., Oakes, D.: Analysis of Survival Data. Chapman and Hall, New York (1984)Google Scholar
  23. 23.
    Epps, T., Pulley, L.: A test for exponentiality vs. monotone hazard alternatives derived from the empirical characteristic function. J. R. Stat. Soc. Ser. B 48(2), 206–213 (1986)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Anderson, T.W., Darling, D.A.: A test of goodness-of-fit. J. Amer. Statist. Assoc. 49, 765–769 (1954)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Maria J. Polidoro
    • 1
    • 4
  • Fernando J. Magalhães
    • 2
    • 4
  • Maria A. Amaral Turkman
    • 3
    • 4
  1. 1.CIICESIESTGF-Polytechnic Institute of PortoFelgueirasPortugal
  2. 2.ISCAP-Polytechnic Institute of PortoPortoPortugal
  3. 3.Faculty of SciencesUniversity of LisboaLisboaPortugal
  4. 4.CEAUL-Center of Statistics and AplicationsUniversity of LisboaLisboaPortugal

Personalised recommendations