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Pseudomartingale estimating equations for modulated renewal process models
Author(s) -
Lin Fengchang,
Fine Jason P.
Publication year - 2009
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00680.x
Subject(s) - semiparametric model , estimator , semiparametric regression , parametric statistics , multiplicative function , mathematics , martingale (probability theory) , realization (probability) , econometrics , asymptotic distribution , estimating equations , consistency (knowledge bases) , computer science , statistics , mathematical analysis , geometry
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.