IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i1d10.1007_s00362-017-0933-5.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0933-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-017-0933-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yoshifumi Ukyo & Hisashi Noma & Kazushi Maruo & Masahiko Gosho, 2019. "Improved Small Sample Inference Methods for a Mixed-Effects Model for Repeated Measures Approach in Incomplete Longitudinal Data Analysis," Stats, MDPI, vol. 2(2), pages 1-15, March.
    2. Feng-Chang Xie & Jin-Guan Lin & Bo-Cheng Wei, 2010. "Testing for varying zero-inflation and dispersion in generalized Poisson regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1509-1522.
    3. Chun-Zheng Cao & Jin-Guan Lin & Li-Xing Zhu, 2010. "Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors," Statistical Papers, Springer, vol. 51(4), pages 813-836, December.
    4. Jin-Guan Lin & Li-Xing Zhu & Chun-Zheng Cao & Yong Li, 2011. "Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1509-1531, August.
    5. 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.
    6. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Homogeneity diagnostics for skew-normal nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 821-827, March.
    7. Baddeley, Adrian & Turner, Rolf & Mateu, Jorge & Bevan, Andrew, 2013. "Hybrids of Gibbs Point Process Models and Their Implementation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i11).
    8. Zhu, Xuehu & Chen, Fei & Guo, Xu & Zhu, Lixing, 2016. "Heteroscedasticity testing for regression models: A dimension reduction-based model adaptive approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 263-283.
    9. Xin-Yu Tian & Xincheng Shi & Cheng Peng & Xiao-Jian Yi, 2021. "A Reliability Growth Process Model with Time-Varying Covariates and Its Application," Mathematics, MDPI, vol. 9(8), pages 1-15, April.
    10. Kang-Ping Lu & Shao-Tung Chang, 2021. "Robust Algorithms for Change-Point Regressions Using the t -Distribution," Mathematics, MDPI, vol. 9(19), pages 1-28, September.
    11. Jin-Guan Lin & Ji Chen & Yong Li, 2012. "Bayesian Analysis of Student t Linear Regression with Unknown Change-Point and Application to Stock Data Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 40(3), pages 203-217, October.
    12. Zhu, Zhongyi & Fung, Wing K., 2004. "Variance component testing in semiparametric mixed models," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 107-118, October.
    13. Wong, Heung & Liu, Feng & Chen, Min & Ip, Wai Cheung, 2009. "Empirical likelihood based diagnostics for heteroscedasticity in partial linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3466-3477, July.
    14. Fernanda Maria Müller & Fábio M Bayer, 2017. "Improved two-component tests in Beta-Skew-t-EGARCH models," Economics Bulletin, AccessEcon, vol. 37(4), pages 2364-2373.
    15. Omerovic, Sanela & Friedl, Herwig & Grün, Bettina, 2022. "Modelling Multiple Regimes in Economic Growth by Mixtures of Generalised Nonlinear Models," Econometrics and Statistics, Elsevier, vol. 22(C), pages 124-135.
    16. Crudu, Federico & Osorio, Felipe, 2020. "Bilinear form test statistics for extremum estimation," Economics Letters, Elsevier, vol. 187(C).
    17. Cordeiro, Gauss M., 2008. "Corrected Maximum Likelihood Estimators in Linear Heteroskedastic Regression Models," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 28(1), May.
    18. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    19. Luigi Augugliaro & Angelo M. Mineo & Ernst C. Wit, 2013. "Differential geometric least angle regression: a differential geometric approach to sparse generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 471-498, June.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:61:y:2020:i:1:d:10.1007_s00362-017-0933-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.