Pseudomartingale estimating equations for modulated renewal process models
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2009 · Volume 71 · Issue 1
DOI: 10.1111/j.1467-9868.2008.00680.x
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.
Keywords
Additive risk model, Earthquake intensity, Ergodicity, Large sample theory, Self-exciting process, Semiparametric epidemic-type aftershock sequence model
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