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Skovgaard's adjustment to likelihood ratio tests in exponential family nonlinear models

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  • Ferrari, Silvia L.P.
  • Cysneiros, Audrey H.M.A.

Abstract

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard's [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28, 3-32] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as [chi]2 with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B 49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265].

Suggested Citation

  • Ferrari, Silvia L.P. & Cysneiros, Audrey H.M.A., 2008. "Skovgaard's adjustment to likelihood ratio tests in exponential family nonlinear models," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3047-3055, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:3047-3055
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    References listed on IDEAS

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    1. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
    2. Cysneiros, Audrey H.M.A. & Ferrari, Silvia L.P., 2006. "An improved likelihood ratio test for varying dispersion in exponential family nonlinear models," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 255-265, February.
    3. Ib M. Skovgaard, 2001. "Likelihood Asymptotics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 3-32, March.
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    1. Melo, Tatiane F.N. & Vasconcellos, Klaus L.P. & Lemonte, Artur J., 2009. "Some restriction tests in a new class of regression models for proportions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3972-3979, October.

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