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Bivariate location–scale models for regression analysis, with applications to lifetime data

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  • Wenqing He
  • Jerald F. Lawless

Abstract

Summary. The literature on multivariate linear regression includes multivariate normal models, models that are used in survival analysis and a variety of models that are used in other areas such as econometrics. The paper considers the class of location–scale models, which includes a large proportion of the preceding models. It is shown that, for complete data, the maximum likelihood estimators for regression coefficients in a linear location–scale framework are consistent even when the joint distribution is misspecified. In addition, gains in efficiency arising from the use of a bivariate model, as opposed to separate univariate models, are studied. A major area of application for multivariate regression models is to clustered, ‘parallel’ lifetime data, so we also study the case of censored responses. Estimators of regression coefficients are no longer consistent under model misspecification, but we give simulation results that show that the bias is small in many practical situations. Gains in efficiency from bivariate models are also examined in the censored data setting. The methodology in the paper is illustrated by using lifetime data from the Diabetic Retinopathy Study.

Suggested Citation

  • Wenqing He & Jerald F. Lawless, 2005. "Bivariate location–scale models for regression analysis, with applications to lifetime data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 63-78, February.
    • Handle: RePEc:bla:jorssb:v:67:y:2005:i:1:p:63-78
    DOI: 10.1111/j.1467-9868.2005.00488.x
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    Cited by:

    1. Gladys Barriga & Francisco Louzada-Neto & Edwin Ortega & Vicente Cancho, 2010. "A bivariate regression model for matched paired survival data: local influence and residual analysis," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 477-495, November.
    2. Lawless, Jerald F. & Yilmaz, Yildiz E., 2011. "Comparison of semiparametric maximum likelihood estimation and two-stage semiparametric estimation in copula models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2446-2455, July.
    3. Côté, Marie-Pier & Genest, Christian & Omelka, Marek, 2019. "Rank-based inference tools for copula regression, with property and casualty insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 1-15.
    4. Wenqing He & Grace Y. Yi, 2020. "Parametric and semiparametric estimation methods for survival data under a flexible class of models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 369-388, April.
    5. Alan T. K. Wan & Jinhong You & Riquan Zhang, 2016. "A Seemingly Unrelated Nonparametric Additive Model with Autoregressive Errors," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 894-928, May.
    6. Wenjing Yin & Sihai Dave Zhao & Feng Liang, 2022. "Bayesian penalized Buckley-James method for high dimensional bivariate censored regression models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 282-318, April.
    7. Manuel Oviedo-de La Fuente & Celestino Ordóñez & Javier Roca-Pardiñas, 2020. "Functional Location-Scale Model to Forecast Bivariate Pollution Episodes," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
    8. Dexen DZ. Xi & C.B. Dean & Stephen W. Taylor, 2020. "Modeling the duration and size of extended attack wildfires as dependent outcomes," Environmetrics, John Wiley & Sons, Ltd., vol. 31(5), August.

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