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Pseudomartingale estimating equations for modulated renewal process models

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  • Fengchang Lin
  • Jason P. Fine

Abstract

Summary. We adapt martingale estimating equations based on gap time information to a general intensity model for a single realization of a modulated renewal process. The consistency and asymptotic normality of the estimators is proved under ergodicity conditions. Previous work has considered either parametric likelihood analysis or semiparametric multiplicative models using partial likelihood. The framework is generally applicable to semiparametric and parametric models, including additive and multiplicative specifications, and periodic models. It facilitates a semiparametric extension of a popular parametric earthquake model. Simulations and empirical analyses of Taiwanese earthquake sequences illustrate the methodology's practical utility.

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  • Fengchang Lin & Jason P. Fine, 2009. "Pseudomartingale estimating equations for modulated renewal process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 3-23, January.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:1:p:3-23
    DOI: 10.1111/j.1467-9868.2008.00680.x
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    References listed on IDEAS

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    1. Robert L. Strawderman, 2005. "The accelerated gap times model," Biometrika, Biometrika Trust, vol. 92(3), pages 647-666, September.
    2. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    3. Jiancang Zhuang, 2006. "Second‐order residual analysis of spatiotemporal point processes and applications in model evaluation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 635-653, September.
    4. D. Zeng & D. Y. Lin, 2007. "Maximum likelihood estimation in semiparametric regression models with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 507-564, September.
    5. Chen, Qingxia & Zeng, Donglin & Ibrahim, Joseph G., 2007. "Sieve Maximum Likelihood Estimation for Regression Models With Covariates Missing at Random," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1309-1317, December.
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    Cited by:

    1. Xin Chen & Jieli Ding & Liuquan Sun, 2018. "A semiparametric additive rate model for a modulated renewal process," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(4), pages 675-698, October.

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