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Size and power properties of some tests in the Birnbaum-Saunders regression model

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  • Lemonte, Artur J.
  • Ferrari, Silvia L.P.

Abstract

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n-1/2 and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications.

Suggested Citation

  • Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Size and power properties of some tests in the Birnbaum-Saunders regression model," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1109-1117, February.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:1109-1117
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    References listed on IDEAS

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    1. Leiva, Victor & Barros, Michelli & Paula, Gilberto A. & Galea, Manuel, 2007. "Influence diagnostics in log-Birnbaum-Saunders regression models with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5694-5707, August.
    2. Chan, P.S. & Ng, H.K.T. & Balakrishnan, N. & Zhou, Q., 2008. "Point and interval estimation for extreme-value regression model under Type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 4040-4058, April.
    3. Lemonte, Artur J. & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2007. "Improved statistical inference for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4656-4681, May.
    4. Xie, Feng-Chang & Wei, Bo-Cheng, 2007. "Diagnostics analysis for log-Birnbaum-Saunders regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4692-4706, May.
    5. Meintanis, Simos G., 2010. "Inference procedures for the Birnbaum-Saunders distribution and its generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 367-373, February.
    6. Wu, Jianrong & Wong, A. C. M., 2004. "Improved interval estimation for the two-parameter Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 809-821, November.
    7. Lemonte, Artur J. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2010. "Improved likelihood inference in Birnbaum-Saunders regressions," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1307-1316, May.
    8. Xu, Ancha & Tang, Yincai, 2010. "Reference analysis for Birnbaum-Saunders distribution," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 185-192, January.
    9. Manuel Galea & Victor Leiva-Sanchez & Gilberto Paula, 2004. "Influence Diagnostics in log-Birnbaum-Saunders Regression Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(9), pages 1049-1064.
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    1. Lemonte, Artur J. & Ferrari, Silvia L.P., 2011. "Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2388-2399, July.
    2. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.
    3. Rafael Farias & Artur Lemonte, 2011. "Bayesian inference for the Birnbaum–Saunders nonlinear regression model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(4), pages 423-438, November.
    4. Lemonte, Artur J., 2013. "On the gradient statistic under model misspecification," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 390-398.
    5. Ortega, Edwin M.M. & Cordeiro, Gauss M. & Lemonte, Artur J., 2012. "A log-linear regression model for the β-Birnbaum–Saunders distribution with censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 698-718.
    6. Li, Ai-Ping & Xie, Feng-Chang, 2012. "Diagnostics for a class of survival regression models with heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4204-4214.

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