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Estimation in some counting process models with multiplicative structure. (English) Zbl 0695.62208
Summary: It is assumed that we observe one realization of an r-dimensional counting process with intensities that are products of a predictable weight process, a common function of time and parameters $$\beta_ i$$, $$i=1,...,r$$, which distinguish the components. Provided the realization observed brings increasing information on $$\beta$$ as the observed time grows, strong consistency of a partial maximum likelihood estimator is proved. For such realizations it is also proved that the estimate, after applying a random normalization, is asymptotically standard normal.
##### MSC:
 62M09 Non-Markovian processes: estimation
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