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Improved heteroskedasticity likelihood ratio tests in symmetric nonlinear regression models

Author

Listed:
  • Mariana C. Araújo

    (Universidade Federal do Rio Grande do Norte)

  • Audrey H. M. A. Cysneiros

    (Universidade Federal de Pernambuco)

  • Lourdes C. Montenegro

    (Universidade Federal de Minas Gerais)

Abstract

In this paper we address the issue of testing inference of the dispersion parameter in heteroscedastic symmetric nonlinear regression models considering small samples. We derive Bartlett corrections to improve the likelihood ratio as well modified profile likelihood ratio tests. Our results extend some of those obtained in Cordeiro (J Stat Comput Simul 74:609–620, 2004) and Ferrari et al. (J Stat Plan Inference 124:423–437, 2004), who consider a symmetric nonlinear regression model and normal linear regression model, respectively. We also present the bootstrap and bootstrap Bartlett corrected likelihood ratio tests. Monte Carlo simulations are carried out to compare the finite sample performances of the three corrected tests and their uncorrected versions. The numerical evidence shows that the corrected modified profile likelihood ratio test, the bootstrap and bootstrap Bartlett corrected likelihood ratio test perform better than the other ones. We also present an empirical application.

Suggested Citation

  • Mariana C. Araújo & Audrey H. M. A. Cysneiros & Lourdes C. Montenegro, 2020. "Improved heteroskedasticity likelihood ratio tests in symmetric nonlinear regression models," Statistical Papers, Springer, vol. 61(1), pages 167-188, February.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0933-5
    DOI: 10.1007/s00362-017-0933-5
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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. Jin-Guan Lin & Li-Xing Zhu & Feng-Chang Xie, 2009. "Heteroscedasticity diagnostics for t linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 59-77, June.
    3. 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.
    4. Jeffrey S. Simonoff & Chih‐Ling Tsai, 1994. "Use of Modified Profile Likelihood for Improved Tests of Constancy of Variance in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 357-370, June.
    5. Stein, Markus Chagas & da Silva, Michel Ferreira & Duczmal, Luiz Henrique, 2014. "Alternatives to the usual likelihood ratio test in mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 184-197.
    6. Melo, Tatiane F.N. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2009. "Improved testing inference in mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2573-2582, May.
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