Estimation in some Counting Process Models with Multiplicative Structure
The Annals of Statistics · 1989 · Volume 17 · Issue 4
Abstract
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 $\beta_i, i = 1, \cdots, r$, which distinguish the components. Provided the realization observed brings increasing information on $\beta$ as the observed time grows, strong consistency of a partial ML estimator is proved. For such realizations it is also proved that the estimate, after applying a random normalization, is asymptotically standard normal.
Keywords
62M09, counting processes, Cox regression model, martingale limit theorems
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